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Results tagged with set-theory
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user 483446
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
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 …
- 2,624
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 …
- 2,624
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 …
- 2,624