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I am interested to know the full range of possibilities for the cofinality type of cuts in an ordered field and in other structures, such as nonstandard models of arithmetic. Definitions. ...

By "formal analogies" between the metamathematics of $\mathsf{ZFC}$/set theory and $\mathsf{PA}$(=Peano Arithmetic)/first order arithmetic, I mean facts such as the following: We are considering a ...

This is a modified version of a question which was asked and bountied at MSE without success. Below, "$\mathsf{PA}$" refers to first-order Peano arithmetic. There are various "...

The following are a collection of doubts, some of which shall have concrete answers while others may have not. Any kind of help will be welcome. Reading Peter Smith's "Gödel Without (Too Many) Tears",...

We know that Con(ZF) implies Con(ZFC+GCH), Con(ZF+neg(AC)) and Con(ZFC+neg(CH)). But what are some weak theories in which these relative independence results are provable? In particular, are they ...

Are there first-order statements that second order PA proves that first order PA does not? Is this known one way or the other? Could you share an example? (edit: to clarify, by 'second order PA' I don'...