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Everyone knows that the real line $\langle\mathbb{R},<\rangle$ is the unique endless complete dense linear order with a countable dense set. Suslin's hypothesis is the question whether we can replace …

In some current work, my co-authors and I had wanted in a certain argument to appeal to $\kappa^{\lt\kappa}=\kappa$ in $L[A]$, in a situation where $A\subset\kappa$ and $\kappa$ was weakly inaccessibl …

It is well-known that an uncountable regular cardinal $\kappa$ is strongly compact if and only if every $\kappa$-complete filter on any set extends to a $\kappa$-complete ultrafilter on that set. The …

This question is related to an issue in my answer to Monroe Eskew's question on the failure of Cantor-Bernstein for the Lévy collapse. Question. Is the Lévy collapse $\text{Coll}(\omega,\lt\kappa)$ …

The question is whether, when you add a Cohen subset to a cardinal $\kappa$, that cardinal becomes a characteristic of the resulting forcing extension $V[G]$. Or can there be strange instances in whic …

Main Question. Can there be an embedding $j:V\to L$ of the set-theoretic universe $V$ to the constructible universe $L$, if $V\neq L$? By embedding here, I mean merely a proper class isomorphism from …