7
votes
1answer
613 views

Some constructive versions of the Continuum Hypothesis are false. Are any true, or open?

Background In constructive set theory (say based on CZF) there are inequivalent ways of stating the continuum hypothesis. Some of them are easily if not trivially refutable with common anti-classical ...
8
votes
3answers
1k views

Is set-induction relatively consistent?

One way to state the axiom of foundation is that the $\in$ relation on any transitive set is well-founded in the following sense: A relation $(X,\prec)$ is well-founded if for any subset $S\subseteq ...
8
votes
3answers
820 views

Intuitionistic Lowenheim-Skolem?

Is there a version of the Löwenheim-Skolem theorem in intuitionistic logic? I'm particularly interested in the "downward" form. The standard proof I know uses the Tarski-Vaught test for ...