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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 votes
0 answers
511 views

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 …
Benedict Eastaugh's user avatar
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 …
Benedict Eastaugh's user avatar
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 …
Benedict Eastaugh's user avatar