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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

Clearing misconceptions: Defining "is a model of ZFC" in ZFC

I suspect these sorts of problems arise in two ways: ignoring wrongness (e.g. Skolem's paradox, that there are countable models of set theory which believe in uncountable sets) and ignoring first-orde …
some guy on the street's user avatar
8 votes
Accepted

Subset of the plane that intersects every line exactly twice

By AC, choose a cardinal well-ordering of the lines in in the plane and any well-ordering of all the points. We proceed by transfinite induction. Suppose $A_l$ is a set of points, no three colinear, …
some guy on the street's user avatar