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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.

8 votes
3 answers
2k views

Surreal Numbers and Set Theory

Hello, I looked through MathOverflow's existing entries but couldn't find a satisfactory answer to the following question: What is the relationship between No, Conway's class of surreal numbers, and …
Alex Lupsasca's user avatar
4 votes

(Non?)-linearity of the consistency strength ordering in ZF

My understanding is that the large cardinals are indeed linearly ordered, which is a remarkable fact. Of course, it is not a theorem (nor could it ever be?), but merely an empirical fact; still, there …
Alex Lupsasca's user avatar
38 votes
5 answers
9k views

Completion of ZFC

I attended a talk given by W. Hugh Woodin regarding the Ultimate L axiom and I wanted to verify my current understanding of what the search for this axiom means. I find it to be a fascinating topic bu …
Alex Lupsasca's user avatar
20 votes
2 answers
4k views

Logically independent but true sentences

My question is of a logical nature and concerns what I perceive to be two different types of mathematical independence. Suppose we have a (sufficiently strong) axiomatic theory $T$. Gödel's Incomplet …
Alex Lupsasca's user avatar
14 votes
1 answer
865 views

Set theoretical realizations of the hidden variables program in quantum mechanics

The hidden variables program in quantum mechanics has been largely discredited by two powerful theorems, namely those of Bell and Kochen/Specker. Nonetheless, this program retains a certain philosophi …
Alex Lupsasca's user avatar