All Questions

Implicit in the technique of forcing is the following relative consistency result: If $\mathfrak M$$\vDash$$T$, and therefore $T$ is consistent (where $\mathfrak M$ is the ground model) then if $\...

As is well known, the following theory is equiconsistent with $PA$: $ZFC$ with the axiom of infinity replaced by its negation. Since this theory is equiconsistent with $PA$, it would seem ...

Tl;dr version: there are two natural classes of cuts in the nonstandard model of arithmetic consisting of the Dedekind-finite sets (if, in fact, they constitute such a model); both these classes are ...