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Results tagged with reference-request
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user 101817
This tag is used if a reference is needed in a paper or textbook on a specific result.
16
votes
Accepted
Do $X$ and $Y$ have the same cardinality if their families of finite subsets do?
It can be proved in $\mathsf{ZF}$ that ``for all cardianls $\mathfrak{a},\mathfrak{b}$, if $\mathrm{fin}(\mathfrak{a})=\mathrm{fin}(\mathfrak{b})$, then $\mathfrak{a}=\mathfrak{b}$'' implies $\mathsf{ …
- 1,782
8
votes
Accepted
Reference request: The non-productivity of Lindenbaum numbers
Karl-Heinz Diener proved in On the transitive hull of a κ‐narrow relation that for all class relations $R$, if $R$ is $\kappa$-narrow in the sense that $\aleph^\ast(R^{-1}[\{x\}])\leqslant\kappa$ for …
- 1,782
4
votes
Terminology for a set that does not surject onto $\omega$ (in ZF)
I suggest the terminology "power Dedekind finite" by Andreas Blass in his paper Power-Dedekind Finiteness, and I use this terminology throughout all my papers. By Kuratowski's celebrated theorem, a se …
- 1,782