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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.
7
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0
answers
511
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Fragments of Morse—Kelley set theory
Morse—Kelley set theory (hereafter MK) is the impredicative counterpart of von Neumann—Bernays—Gödel set theory (NBG), where formulas containing class quantifiers are permitted in the comprehension sc …
10
votes
How much choice is needed to show that formally real fields can be ordered?
Let me give an answer from a different perspective. Konrad Swanepoel's accepted answer shows what happens in the general case, for formally real fields of any cardinality. However, it is possible to c …
10
votes
Ultrainfinitism, or a step beyond the transfinite
Perhaps you could take a look at William Reinhardt's paper 'Remarks on reflection principles, large cardinals, and elementary embeddings' (1974). Reinhardt suggests extending the set-theoretic univers …