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How much "finitary combinatorics" can be emulated by an infinite Dedekind-finite set?
Throughout, we work in $\mathsf{ZF}$. Let $[n]=\{1,...,n\}$. Given a set $X$ and a first-order sentence $\varphi$, let $M_X(\varphi)$ be the set of isomorphism types of models of $\varphi$ with ...
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