Are there any known statements that are provably independent of $ZF + V=L$? A similar question was asked here but focusing on "interesting" statements and all examples of statement …

Can one prove the Cantor-Bernstein (or Schröder-Bernstein) theorem without using the Axiom of Infinity?

This question is of course inspired by http://mathoverflow.net/questions/17605/how-to-solve-ffx-cosx and Joel David Hamkins' answer, which somehow gives a formal trick for solving …

There are collections too big to be a set, e.g. the collection of all sets (in ZFC), and there are collections that cannot be sets for "pure" logical reasons, e.g. the collection o …

If ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice) is consistent, does it remain consistent when the following statement is added to it as a new axiom? "There exists a …

Measure theory is somewhat focused on the cardinal $\aleph_0$: First of all we have the usual $\sigma$-additivity, Polish (separable!) spaces such as $\mathbb{R}^n$, countable sequ …

Sorry if this is a silly question. I was wondering, under what axioms of set theory is it true that if $\alpha$,$\beta$ are cardinals, and $2^\alpha=2^\beta$, then $\alpha=\beta$? …

Background The beth function is defined recursively by: $\beth_0 = \aleph_0$, $\beth_{\alpha + 1} = 2^{\beth_\alpha}$, and $\beth_\lambda = \bigcup_{\alpha < \lambda} \beth_\al …

The Cartesian product of two empty sets is the singleton set $\{ () \}$ containing the empty tuple. So, given a set $A$ which is empty, $A \times A $ is defined as: $$ A \times A = …

How many field automorphisms does $\mathbf{C}$ have? If you assume the axiom of choice, there are tons of them -- $2^{2^{\aleph_0}}$ I believe. And what if you don't -- how essen …

I'd like to write down a proof of the following (simple) fact: $\forall x\left(\bigcup\left\{x\right\}=x\right)$. I'd like to use the rules of inference of natural deduction. One c …

In the paper "Complete topoi representing models of set theory" by Blass and Scedrov, they consider a general notion of Boolean-valued model of set theory, and one of the condition …

"Let Top be the category of topological spaces." If I see a definition like this, in which homeomorphic (isomorphic in the category) spaces are not identified together, then for ea …

Every group presentation determines the corresponding Cayley graph, which has a node for each group element, and arrows labeled with the generators to get from one group element to …

Frequently it is useful do deal with countable transitive models M of ZFC, for example in forcing constructions. The notion of being an ordinal is absolute for any transitive mo …