Every now and then, somebody will tell me about a question. When I start thinking about it, they say, "actually, it's undecidable in ZFC." For example, suppose A is an abelian gro …

The goal of this question is to recall a certain mathematical fact -not in my field- that I was once briefly told and that I have fogotten, and also to collect similar results. T …

Background and Motivation I've always been fascinated about algebraic statements independent from ZFC set theory. One such fascinating example comes from considering $\rm{Ext}^1_\ …

This problem was posed on Math StackExchange some time ago, but it did not garner any solutions there. I think that it is interesting enough to be posed here on Math Overflow, so h …

I am looking for sentences in the language of first order arithmetic ($0,1,+,\cdot,\leq$) which are independent from $\Pi^0_2$ consequences of true arithmetic $\Pi^0_2\text{-}\math …

Is it possible to prove $Con(ZFC) \rightarrow Con(ZFC + \neg CH)$ purely within ZFC? To prove this (using forcing) one seems to need a countable transitive model of ZFC. The texts …

Short version: Is the axiom of union independent of the rest of axioms of ZF? NO) Tourlakis (2003) says in p. 177 that the axiom of union can be derived from the rest of ZF if an …

Given any reasonable formal system F (e.g., Peano Arithmetic or ZFC), we all know that one can construct a Turing machine that runs forever iff F is consistent, by enumerating the …

Just a curiosity: Is there an assertion of which a proof (formalizable, say, in ZFC) is not known but a proof that it's not undecidable (in ZFC) is known? Edit: after the com …

what is the inequality in terms of n to find the independence number of G where G is C2n+1. what is the inequality in terms of n to find the independence number of G where G' (G c …

A non-principal ultrafilter $\mathcal{U}$ on $\omega$ is a p-point (or weakly selective) iff for every partition $\omega = \bigsqcup _{n < \omega} Z_n$ into null sets, i.e each …

Hello all, one may look for "minimal system of axioms" for ZFC (or any other theory) in the following (unusual) sense : say that a subset S of ZFC is "sufficient" if there is an ex …

I'm looking for references for the following facts concerning the ultrafilter lemma (~ "there exist non-principal ultrafilters"): The ultrafilter lemma is independent of ZF. ZF …

In order to get the relative consistency of some statement, it suffices to find a notion of forcing, and a condition $p$ in that forcing, such that $p$ forces the desired statement …

Suslin's problem is: Given a complete dense linear order without endpoints, if it has the ccc must it be isomorphic to $\mathbb{R}$? The answer is that it's independent of ZF …