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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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Axiom of Choice : Reasons behind using it or avoiding it? [duplicate]

I am a 1st year PhD student in Mathematics. During my masters course in Ring theory, the proof of the result : Every commutative unital ring has a maximal ideal was done in the class. Every proof of i …
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