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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
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Why do we ignore non-standard finite sets in ordinary mathematics?
Here is a how a typical proof might look like in group theory--- Suppose we are given a finite group $G$. Enumerate the elements $g_1, \dots, g_n$. Now consider a formula $\phi(g_1, \dots, g_n)$ which …
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Seemingly complex logic/set-theoretic puzzle
Based on the answers proposed to this question, I think this problem is ill-defined. The set of possible questions and assignment of truth valuations is not well defined. A fair definition of a "quest …