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 ...
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 ...
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 ...