Mixing
Cardinality of $[lambda]^kappa$
$begingroup$
Let $kappa leq lambda$ cardinals with $lambda$ infinite, and $[lambda]^kappa={Ysubseteqlambda : ot(Y,in)=kappa}$. I want to show that $[lambda]^kappa asymp ^kappalambda$.
I've aldredy proved that $[lambda]^kappa asymp {f in ^kappalambda: f text{is increasing}}$, and so easily $[lambda]^kappapreceq ^kappalambda$.
For the other injective function I don't have any ideas: tryng to associate the function to its range dosen't work, because I find only subset with cardinality $kappa$ but not with order type $kappa$.
Do you have some suggestions?
elementary-set-theory cardinals
asked Jan 22 at 19:19
MarcoMMarcoM
104
$endgroup$
add a comment |
$begingroup$
Let $kappa leq lambda$ cardinals with $lambda$ infinite, and $[lambda]^kappa={Ysubseteqlambda : ot(Y,in)=kappa}$. I want to show that $[lambda]^kappa asymp ^kappalambda$.
I've aldredy proved that $[lambda]^kappa asymp {f in ^kappalambda: f text{is increasing}}$, and so easily $[lambda]^kappapreceq ^kappalambda$.
For the other injective function I don't have any ideas: tryng to associate the function to its range dosen't work, because I find only subset with cardinality $kappa$ but not with order type $kappa$.
Do you have some suggestions?
elementary-set-theory cardinals
asked Jan 22 at 19:19
MarcoMMarcoM
104
$endgroup$
add a comment |
$begingroup$
Let $kappa leq lambda$ cardinals with $lambda$ infinite, and $[lambda]^kappa={Ysubseteqlambda : ot(Y,in)=kappa}$. I want to show that $[lambda]^kappa asymp ^kappalambda$.
I've aldredy proved that $[lambda]^kappa asymp {f in ^kappalambda: f text{is increasing}}$, and so easily $[lambda]^kappapreceq ^kappalambda$.
For the other injective function I don't have any ideas: tryng to associate the function to its range dosen't work, because I find only subset with cardinality $kappa$ but not with order type $kappa$.
Do you have some suggestions?
elementary-set-theory cardinals
asked Jan 22 at 19:19
MarcoMMarcoM
104
$endgroup$
Let $kappa leq lambda$ cardinals with $lambda$ infinite, and $[lambda]^kappa={Ysubseteqlambda : ot(Y,in)=kappa}$. I want to show that $[lambda]^kappa asymp ^kappalambda$.
I've aldredy proved that $[lambda]^kappa asymp {f in ^kappalambda: f text{is increasing}}$, and so easily $[lambda]^kappapreceq ^kappalambda$.
For the other injective function I don't have any ideas: tryng to associate the function to its range dosen't work, because I find only subset with cardinality $kappa$ but not with order type $kappa$.
Do you have some suggestions?
elementary-set-theory cardinals
elementary-set-theory cardinals
asked Jan 22 at 19:19
MarcoMMarcoM
104
asked Jan 22 at 19:19
MarcoMMarcoM
104
asked Jan 22 at 19:19
MarcoMMarcoM
104
asked Jan 22 at 19:19
MarcoMMarcoM
104
asked Jan 22 at 19:19
MarcoMMarcoM
104
104
add a comment |
add a comment |
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