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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.
4
votes
Candidate "AEC-yielding" fragments of bad logics
It's been so long since I've seen a good AEC question on here! In fact, so long I forgot the account info that gives me enough reputation to post this as a comment.
I think this will get you rather c …
3
votes
Compatibility of Łośian phenomena in second-order logic
I'm not sure I have a definitive answer, but three nice observations that are too long for comments:
If you relax from ultrafilters to extenders (seen as directed systems of ultrafilters), then there …
3
votes
Accepted
Vopěnka's Principle for non-first-order logics
This is a really late answer, but the answer to your question is "No." As a dual to the Theorem 6 that Thomas Benjamin mentions above (which I believe is a result of Stavi), Janos Makowsky proved tha …