Mixing
Terminology about trees
$begingroup$
In set theory, a tree is usually defined as a partial order such that the set of elements below any given one is well-ordered. I am interested in the class of partial orders $P$ such that for every $p in P$, the set of $q leq p$ is just linearly ordered. Does this have a name?
set-theory terminology posets trees
asked Jan 18 at 12:42
Monroe EskewMonroe Eskew
7,75512159
$endgroup$
add a comment |
$begingroup$
In set theory, a tree is usually defined as a partial order such that the set of elements below any given one is well-ordered. I am interested in the class of partial orders $P$ such that for every $p in P$, the set of $q leq p$ is just linearly ordered. Does this have a name?
set-theory terminology posets trees
asked Jan 18 at 12:42
Monroe EskewMonroe Eskew
7,75512159
$endgroup$
1
$begingroup$
rd.springer.com/article/10.1007/BF00571186
$endgroup$
– Asaf Karagila
Jan 18 at 15:45
1
$begingroup$
Prefix orders seem to be relevant, if for no other reason than they appear to fit the required definitional niche. See en.m.wikipedia.org/wiki/Prefix_order
$endgroup$
– Not Mike
Jan 18 at 17:18
$begingroup$
Thanks @NotMike! It's nice to see this coming from outside of pure set theory. Feel free to put this as an answer.
$endgroup$
– Monroe Eskew
Jan 18 at 17:26
$begingroup$
Adeleke and Neumann have a Memoir of the AMS 'Relations related to betweenness' which considers various structures along these lines. In particular, a partially ordered set satisfying the property above which is also assumed to be connected (every pair of elements has a common lower bound) is called a semilinearly ordered set. I don't know if they have a name for such objects if they're not connected.
$endgroup$
– shane.orourke
Jan 18 at 19:22
add a comment |
$begingroup$
In set theory, a tree is usually defined as a partial order such that the set of elements below any given one is well-ordered. I am interested in the class of partial orders $P$ such that for every $p in P$, the set of $q leq p$ is just linearly ordered. Does this have a name?
set-theory terminology posets trees
asked Jan 18 at 12:42
Monroe EskewMonroe Eskew
7,75512159
$endgroup$
In set theory, a tree is usually defined as a partial order such that the set of elements below any given one is well-ordered. I am interested in the class of partial orders $P$ such that for every $p in P$, the set of $q leq p$ is just linearly ordered. Does this have a name?
set-theory terminology posets trees
set-theory terminology posets trees
asked Jan 18 at 12:42
Monroe EskewMonroe Eskew
7,75512159
asked Jan 18 at 12:42
Monroe EskewMonroe Eskew
7,75512159
edited Jan 18 at 15:32
Monroe Eskew
asked Jan 18 at 12:42
Monroe EskewMonroe Eskew
7,75512159
asked Jan 18 at 12:42
Monroe EskewMonroe Eskew
7,75512159
asked Jan 18 at 12:42
Monroe EskewMonroe Eskew
7,75512159
7,75512159
1
$begingroup$
rd.springer.com/article/10.1007/BF00571186
$endgroup$
– Asaf Karagila
Jan 18 at 15:45
1
$begingroup$
Prefix orders seem to be relevant, if for no other reason than they appear to fit the required definitional niche. See en.m.wikipedia.org/wiki/Prefix_order
$endgroup$
– Not Mike
Jan 18 at 17:18
$begingroup$
Thanks @NotMike! It's nice to see this coming from outside of pure set theory. Feel free to put this as an answer.
$endgroup$
– Monroe Eskew
Jan 18 at 17:26
$begingroup$
Adeleke and Neumann have a Memoir of the AMS 'Relations related to betweenness' which considers various structures along these lines. In particular, a partially ordered set satisfying the property above which is also assumed to be connected (every pair of elements has a common lower bound) is called a semilinearly ordered set. I don't know if they have a name for such objects if they're not connected.
$endgroup$
– shane.orourke
Jan 18 at 19:22
add a comment |
1
$begingroup$
rd.springer.com/article/10.1007/BF00571186
$endgroup$
– Asaf Karagila
Jan 18 at 15:45
1
$begingroup$
Prefix orders seem to be relevant, if for no other reason than they appear to fit the required definitional niche. See en.m.wikipedia.org/wiki/Prefix_order
$endgroup$
– Not Mike
Jan 18 at 17:18
$begingroup$
Thanks @NotMike! It's nice to see this coming from outside of pure set theory. Feel free to put this as an answer.
$endgroup$
– Monroe Eskew
Jan 18 at 17:26
$begingroup$
Adeleke and Neumann have a Memoir of the AMS 'Relations related to betweenness' which considers various structures along these lines. In particular, a partially ordered set satisfying the property above which is also assumed to be connected (every pair of elements has a common lower bound) is called a semilinearly ordered set. I don't know if they have a name for such objects if they're not connected.
$endgroup$
– shane.orourke
Jan 18 at 19:22
1
1
$begingroup$
rd.springer.com/article/10.1007/BF00571186
$endgroup$
– Asaf Karagila
Jan 18 at 15:45
$begingroup$
rd.springer.com/article/10.1007/BF00571186
$endgroup$
– Asaf Karagila
Jan 18 at 15:45
1
1
$begingroup$
Prefix orders seem to be relevant, if for no other reason than they appear to fit the required definitional niche. See en.m.wikipedia.org/wiki/Prefix_order
$endgroup$
– Not Mike
Jan 18 at 17:18
$begingroup$
Prefix orders seem to be relevant, if for no other reason than they appear to fit the required definitional niche. See en.m.wikipedia.org/wiki/Prefix_order
$endgroup$
– Not Mike
Jan 18 at 17:18
$begingroup$
Thanks @NotMike! It's nice to see this coming from outside of pure set theory. Feel free to put this as an answer.
$endgroup$
– Monroe Eskew
Jan 18 at 17:26
$begingroup$
Thanks @NotMike! It's nice to see this coming from outside of pure set theory. Feel free to put this as an answer.
$endgroup$
– Monroe Eskew
Jan 18 at 17:26
$begingroup$
Adeleke and Neumann have a Memoir of the AMS 'Relations related to betweenness' which considers various structures along these lines. In particular, a partially ordered set satisfying the property above which is also assumed to be connected (every pair of elements has a common lower bound) is called a semilinearly ordered set. I don't know if they have a name for such objects if they're not connected.
$endgroup$
– shane.orourke
Jan 18 at 19:22
$begingroup$
Adeleke and Neumann have a Memoir of the AMS 'Relations related to betweenness' which considers various structures along these lines. In particular, a partially ordered set satisfying the property above which is also assumed to be connected (every pair of elements has a common lower bound) is called a semilinearly ordered set. I don't know if they have a name for such objects if they're not connected.
$endgroup$
– shane.orourke
Jan 18 at 19:22
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
They are also called trees.
In that terminology, trees of your first kind are known as the well-founded trees, since they are trees where the tree order is well-founded (and well-founded linear orders are the same as well-orders).
I think that the situation is that because set theorists are mainly interested in the well-founded case, the terminology evolved to drop the adjective from well-founded trees.
There are many competing definitions of tree in mathematics, not all equivalent. For graph-theorists, for example, a tree is a certain kind of cycle-free graph.
answered Jan 18 at 13:26
Joel David HamkinsJoel David Hamkins
165k25503875
$endgroup$
1
$begingroup$
This is also what I thought off the top of my head, but Jech, Kunen, and Kanamori all put well-foundedness into the definition of a tree. Do you know of a reference the defines trees as the more general class?
$endgroup$
– Monroe Eskew
Jan 18 at 15:32
1
$begingroup$
I guess the complication also is that "well-founded tree" now means something else in set theory, where the tree is growing downward and has no infinite branches.
$endgroup$
– Joel David Hamkins
Jan 18 at 17:58
2
$begingroup$
For one reference: Keisler uses the linear order definition in his article "Models with tree structures". Full citation: H. Jerome Keisler. “Models with tree structures”. In: Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) . Amer. Math. Soc., Providence, R.I., 1974, pp. 331–348.
$endgroup$
– Kameryn Williams
Jan 18 at 22:27
1
$begingroup$
But set-theoreticians, who use the word "tree" to mean well-founded tree, must occasionally have to refer to the more general trees. What do they call them? If I use "tree" to mean a poset in which the predecessors of any element are well-ordered, then what should I call a poset in which the predecessors of any element are linearly ordered? I have some vague recollection of hearing them called "pseudotrees" or something like that.
$endgroup$
– bof
Jan 23 at 5:58
2
$begingroup$
@bof A colleague pointed me to several set-theory papers by Koppelberg-Monk, Bekkali, and Alos-Ferrer and Ritzberger, where the term pseudotree is used for exactly this kind of poset.
$endgroup$
– Monroe Eskew
Jan 24 at 9:36
|
show 3 more comments
$begingroup$
Upgraded from a comment:
After a little bit of searching, the notion of prefix order seems to be relevant; if for no other reason than that it appears to fit the required definitional niche.
(Also, it seemed worth pointing out the notion of prefix-order is precisely that of a "first-order tree".)
answered Jan 18 at 19:19
Not MikeNot Mike
1,3651528
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "504"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f321178%2fterminology-about-trees%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
They are also called trees.
In that terminology, trees of your first kind are known as the well-founded trees, since they are trees where the tree order is well-founded (and well-founded linear orders are the same as well-orders).
I think that the situation is that because set theorists are mainly interested in the well-founded case, the terminology evolved to drop the adjective from well-founded trees.
There are many competing definitions of tree in mathematics, not all equivalent. For graph-theorists, for example, a tree is a certain kind of cycle-free graph.
answered Jan 18 at 13:26
Joel David HamkinsJoel David Hamkins
165k25503875
$endgroup$
1
$begingroup$
This is also what I thought off the top of my head, but Jech, Kunen, and Kanamori all put well-foundedness into the definition of a tree. Do you know of a reference the defines trees as the more general class?
$endgroup$
– Monroe Eskew
Jan 18 at 15:32
1
$begingroup$
I guess the complication also is that "well-founded tree" now means something else in set theory, where the tree is growing downward and has no infinite branches.
$endgroup$
– Joel David Hamkins
Jan 18 at 17:58
2
$begingroup$
For one reference: Keisler uses the linear order definition in his article "Models with tree structures". Full citation: H. Jerome Keisler. “Models with tree structures”. In: Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) . Amer. Math. Soc., Providence, R.I., 1974, pp. 331–348.
$endgroup$
– Kameryn Williams
Jan 18 at 22:27
1
$begingroup$
But set-theoreticians, who use the word "tree" to mean well-founded tree, must occasionally have to refer to the more general trees. What do they call them? If I use "tree" to mean a poset in which the predecessors of any element are well-ordered, then what should I call a poset in which the predecessors of any element are linearly ordered? I have some vague recollection of hearing them called "pseudotrees" or something like that.
$endgroup$
– bof
Jan 23 at 5:58
2
$begingroup$
@bof A colleague pointed me to several set-theory papers by Koppelberg-Monk, Bekkali, and Alos-Ferrer and Ritzberger, where the term pseudotree is used for exactly this kind of poset.
$endgroup$
– Monroe Eskew
Jan 24 at 9:36
|
show 3 more comments
$begingroup$
They are also called trees.
In that terminology, trees of your first kind are known as the well-founded trees, since they are trees where the tree order is well-founded (and well-founded linear orders are the same as well-orders).
I think that the situation is that because set theorists are mainly interested in the well-founded case, the terminology evolved to drop the adjective from well-founded trees.
There are many competing definitions of tree in mathematics, not all equivalent. For graph-theorists, for example, a tree is a certain kind of cycle-free graph.
answered Jan 18 at 13:26
Joel David HamkinsJoel David Hamkins
165k25503875
$endgroup$
1
$begingroup$
This is also what I thought off the top of my head, but Jech, Kunen, and Kanamori all put well-foundedness into the definition of a tree. Do you know of a reference the defines trees as the more general class?
$endgroup$
– Monroe Eskew
Jan 18 at 15:32
1
$begingroup$
I guess the complication also is that "well-founded tree" now means something else in set theory, where the tree is growing downward and has no infinite branches.
$endgroup$
– Joel David Hamkins
Jan 18 at 17:58
2
$begingroup$
For one reference: Keisler uses the linear order definition in his article "Models with tree structures". Full citation: H. Jerome Keisler. “Models with tree structures”. In: Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) . Amer. Math. Soc., Providence, R.I., 1974, pp. 331–348.
$endgroup$
– Kameryn Williams
Jan 18 at 22:27
1
$begingroup$
But set-theoreticians, who use the word "tree" to mean well-founded tree, must occasionally have to refer to the more general trees. What do they call them? If I use "tree" to mean a poset in which the predecessors of any element are well-ordered, then what should I call a poset in which the predecessors of any element are linearly ordered? I have some vague recollection of hearing them called "pseudotrees" or something like that.
$endgroup$
– bof
Jan 23 at 5:58
2
$begingroup$
@bof A colleague pointed me to several set-theory papers by Koppelberg-Monk, Bekkali, and Alos-Ferrer and Ritzberger, where the term pseudotree is used for exactly this kind of poset.
$endgroup$
– Monroe Eskew
Jan 24 at 9:36
|
show 3 more comments
$begingroup$
They are also called trees.
In that terminology, trees of your first kind are known as the well-founded trees, since they are trees where the tree order is well-founded (and well-founded linear orders are the same as well-orders).
I think that the situation is that because set theorists are mainly interested in the well-founded case, the terminology evolved to drop the adjective from well-founded trees.
There are many competing definitions of tree in mathematics, not all equivalent. For graph-theorists, for example, a tree is a certain kind of cycle-free graph.
answered Jan 18 at 13:26
Joel David HamkinsJoel David Hamkins
165k25503875
$endgroup$
They are also called trees.
In that terminology, trees of your first kind are known as the well-founded trees, since they are trees where the tree order is well-founded (and well-founded linear orders are the same as well-orders).
I think that the situation is that because set theorists are mainly interested in the well-founded case, the terminology evolved to drop the adjective from well-founded trees.
There are many competing definitions of tree in mathematics, not all equivalent. For graph-theorists, for example, a tree is a certain kind of cycle-free graph.
answered Jan 18 at 13:26
Joel David HamkinsJoel David Hamkins
165k25503875
answered Jan 18 at 13:26
Joel David HamkinsJoel David Hamkins
165k25503875
answered Jan 18 at 13:26
Joel David HamkinsJoel David Hamkins
165k25503875
answered Jan 18 at 13:26
Joel David HamkinsJoel David Hamkins
165k25503875
165k25503875
1
$begingroup$
This is also what I thought off the top of my head, but Jech, Kunen, and Kanamori all put well-foundedness into the definition of a tree. Do you know of a reference the defines trees as the more general class?
$endgroup$
– Monroe Eskew
Jan 18 at 15:32
1
$begingroup$
I guess the complication also is that "well-founded tree" now means something else in set theory, where the tree is growing downward and has no infinite branches.
$endgroup$
– Joel David Hamkins
Jan 18 at 17:58
2
$begingroup$
For one reference: Keisler uses the linear order definition in his article "Models with tree structures". Full citation: H. Jerome Keisler. “Models with tree structures”. In: Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) . Amer. Math. Soc., Providence, R.I., 1974, pp. 331–348.
$endgroup$
– Kameryn Williams
Jan 18 at 22:27
1
$begingroup$
But set-theoreticians, who use the word "tree" to mean well-founded tree, must occasionally have to refer to the more general trees. What do they call them? If I use "tree" to mean a poset in which the predecessors of any element are well-ordered, then what should I call a poset in which the predecessors of any element are linearly ordered? I have some vague recollection of hearing them called "pseudotrees" or something like that.
$endgroup$
– bof
Jan 23 at 5:58
2
$begingroup$
@bof A colleague pointed me to several set-theory papers by Koppelberg-Monk, Bekkali, and Alos-Ferrer and Ritzberger, where the term pseudotree is used for exactly this kind of poset.
$endgroup$
– Monroe Eskew
Jan 24 at 9:36
|
show 3 more comments
1
$begingroup$
This is also what I thought off the top of my head, but Jech, Kunen, and Kanamori all put well-foundedness into the definition of a tree. Do you know of a reference the defines trees as the more general class?
$endgroup$
– Monroe Eskew
Jan 18 at 15:32
1
$begingroup$
I guess the complication also is that "well-founded tree" now means something else in set theory, where the tree is growing downward and has no infinite branches.
$endgroup$
– Joel David Hamkins
Jan 18 at 17:58
2
$begingroup$
For one reference: Keisler uses the linear order definition in his article "Models with tree structures". Full citation: H. Jerome Keisler. “Models with tree structures”. In: Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) . Amer. Math. Soc., Providence, R.I., 1974, pp. 331–348.
$endgroup$
– Kameryn Williams
Jan 18 at 22:27
1
$begingroup$
But set-theoreticians, who use the word "tree" to mean well-founded tree, must occasionally have to refer to the more general trees. What do they call them? If I use "tree" to mean a poset in which the predecessors of any element are well-ordered, then what should I call a poset in which the predecessors of any element are linearly ordered? I have some vague recollection of hearing them called "pseudotrees" or something like that.
$endgroup$
– bof
Jan 23 at 5:58
2
$begingroup$
@bof A colleague pointed me to several set-theory papers by Koppelberg-Monk, Bekkali, and Alos-Ferrer and Ritzberger, where the term pseudotree is used for exactly this kind of poset.
$endgroup$
– Monroe Eskew
Jan 24 at 9:36
1
1
$begingroup$
This is also what I thought off the top of my head, but Jech, Kunen, and Kanamori all put well-foundedness into the definition of a tree. Do you know of a reference the defines trees as the more general class?
$endgroup$
– Monroe Eskew
Jan 18 at 15:32
$begingroup$
This is also what I thought off the top of my head, but Jech, Kunen, and Kanamori all put well-foundedness into the definition of a tree. Do you know of a reference the defines trees as the more general class?
$endgroup$
– Monroe Eskew
Jan 18 at 15:32
1
1
$begingroup$
I guess the complication also is that "well-founded tree" now means something else in set theory, where the tree is growing downward and has no infinite branches.
$endgroup$
– Joel David Hamkins
Jan 18 at 17:58
$begingroup$
I guess the complication also is that "well-founded tree" now means something else in set theory, where the tree is growing downward and has no infinite branches.
$endgroup$
– Joel David Hamkins
Jan 18 at 17:58
2
2
$begingroup$
For one reference: Keisler uses the linear order definition in his article "Models with tree structures". Full citation: H. Jerome Keisler. “Models with tree structures”. In: Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) . Amer. Math. Soc., Providence, R.I., 1974, pp. 331–348.
$endgroup$
– Kameryn Williams
Jan 18 at 22:27
$begingroup$
For one reference: Keisler uses the linear order definition in his article "Models with tree structures". Full citation: H. Jerome Keisler. “Models with tree structures”. In: Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) . Amer. Math. Soc., Providence, R.I., 1974, pp. 331–348.
$endgroup$
– Kameryn Williams
Jan 18 at 22:27
1
1
$begingroup$
But set-theoreticians, who use the word "tree" to mean well-founded tree, must occasionally have to refer to the more general trees. What do they call them? If I use "tree" to mean a poset in which the predecessors of any element are well-ordered, then what should I call a poset in which the predecessors of any element are linearly ordered? I have some vague recollection of hearing them called "pseudotrees" or something like that.
$endgroup$
– bof
Jan 23 at 5:58
$begingroup$
But set-theoreticians, who use the word "tree" to mean well-founded tree, must occasionally have to refer to the more general trees. What do they call them? If I use "tree" to mean a poset in which the predecessors of any element are well-ordered, then what should I call a poset in which the predecessors of any element are linearly ordered? I have some vague recollection of hearing them called "pseudotrees" or something like that.
$endgroup$
– bof
Jan 23 at 5:58
2
2
$begingroup$
@bof A colleague pointed me to several set-theory papers by Koppelberg-Monk, Bekkali, and Alos-Ferrer and Ritzberger, where the term pseudotree is used for exactly this kind of poset.
$endgroup$
– Monroe Eskew
Jan 24 at 9:36
$begingroup$
@bof A colleague pointed me to several set-theory papers by Koppelberg-Monk, Bekkali, and Alos-Ferrer and Ritzberger, where the term pseudotree is used for exactly this kind of poset.
$endgroup$
– Monroe Eskew
Jan 24 at 9:36
|
show 3 more comments
$begingroup$
Upgraded from a comment:
After a little bit of searching, the notion of prefix order seems to be relevant; if for no other reason than that it appears to fit the required definitional niche.
(Also, it seemed worth pointing out the notion of prefix-order is precisely that of a "first-order tree".)
answered Jan 18 at 19:19
Not MikeNot Mike
1,3651528
$endgroup$
add a comment |
$begingroup$
Upgraded from a comment:
After a little bit of searching, the notion of prefix order seems to be relevant; if for no other reason than that it appears to fit the required definitional niche.
(Also, it seemed worth pointing out the notion of prefix-order is precisely that of a "first-order tree".)
answered Jan 18 at 19:19
Not MikeNot Mike
1,3651528
$endgroup$
add a comment |
$begingroup$
Upgraded from a comment:
After a little bit of searching, the notion of prefix order seems to be relevant; if for no other reason than that it appears to fit the required definitional niche.
(Also, it seemed worth pointing out the notion of prefix-order is precisely that of a "first-order tree".)
answered Jan 18 at 19:19
Not MikeNot Mike
1,3651528
$endgroup$
Upgraded from a comment:
After a little bit of searching, the notion of prefix order seems to be relevant; if for no other reason than that it appears to fit the required definitional niche.
(Also, it seemed worth pointing out the notion of prefix-order is precisely that of a "first-order tree".)
answered Jan 18 at 19:19
Not MikeNot Mike
1,3651528
answered Jan 18 at 19:19
Not MikeNot Mike
1,3651528
answered Jan 18 at 19:19
Not MikeNot Mike
1,3651528
answered Jan 18 at 19:19
Not MikeNot Mike
1,3651528
1,3651528
add a comment |
add a comment |
Thanks for contributing an answer to MathOverflow!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f321178%2fterminology-about-trees%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
rd.springer.com/article/10.1007/BF00571186
$endgroup$
– Asaf Karagila
Jan 18 at 15:45
1
$begingroup$
Prefix orders seem to be relevant, if for no other reason than they appear to fit the required definitional niche. See en.m.wikipedia.org/wiki/Prefix_order
$endgroup$
– Not Mike
Jan 18 at 17:18
$begingroup$
Thanks @NotMike! It's nice to see this coming from outside of pure set theory. Feel free to put this as an answer.
$endgroup$
– Monroe Eskew
Jan 18 at 17:26
$begingroup$
Adeleke and Neumann have a Memoir of the AMS 'Relations related to betweenness' which considers various structures along these lines. In particular, a partially ordered set satisfying the property above which is also assumed to be connected (every pair of elements has a common lower bound) is called a semilinearly ordered set. I don't know if they have a name for such objects if they're not connected.
$endgroup$
– shane.orourke
Jan 18 at 19:22