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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

Strong extensionality of 'membership' relation defined on the set of all morphisms of a well...

By definition of your relation $\in_C$, only for the morphisms into the terminal object $b:A \to 1$ are there morphisms $a:1 \to A$ such that $a \in_C b$, and $a$ by definition has to be a global elem …
Madeleine Birchfield's user avatar
10 votes
1 answer
575 views

Universal property of the set of injections in the category of sets

Given two sets $A$ and $B$, the function set $B^A$ is characterized by the universal property that the functor $(-)^A:\mathrm{Set} \to \mathrm{Set}$ is the right adjoint of the functor $(-)\times A:\m …
Madeleine Birchfield's user avatar
7 votes
1 answer
306 views

Does a tight apartness relation on a subobject classifier imply the elementary topos is Bool...

Given a set $S$, a tight apartness relation on $S$ is a relation $\#$ which is tight, irreflexive, symmetric, and weakly linear, or more specifically, a relation $\#$ such that for all elements $a \i …
Madeleine Birchfield's user avatar