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Can you remove all the extra arithmetic from ZFC (or other theories)?
Let $\mathbb{N}$ be the standard model of the natural numbers. For any statement in the language of arithmetic, we can translate into a statement in the language of set theory by asking if it is true ...
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Is there any set theory $T$ such that $T$ plus true arithmetic is complete with respect to statements in set theory?
Is there an effective set theory $T$ such that $T + $$TA$ is consistient and complete. It should at least prove all theorems of $ZF$ true, so that it is a "standard" set theory. In particular, the ...