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Results tagged with lo.logic
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user 471475
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
4
votes
1
answer
182
views
Group objects via diagrams or generalized elements — Kripke–Joyal?
The notion of a group object $G$ in a category with finite products can either be defined with a few commutative diagrams or via requiring that each hom set $\hom(X,G)$ is a group. There is a theorem …
- 723
5
votes
1
answer
256
views
Internal language proof of Lawvere's fixed point theorem for cartesian closed categories
This proof of Lawvere's fixed point theorem suggests (since it uses $\lambda$ notation) that it is written in the internal language of cartesian closed categories (which is the $\lambda$-calculus, as …
- 723
12
votes
1
answer
410
views
Definition of "classifying topos"
Is there a geometric theory $T$ and a Grothendieck topos $\mathcal E$ such that (2) holds but (1) doesn't:
$\mathcal E$ 2-represents the 2-functor
$$\mathbf{GrothTop}\to\mathbf{Cat}$$
which sends a G …
- 723
16
votes
2
answers
1k
views
Major applications of the internal language of toposes
What are the major applications of the internal language of toposes?
Here are a few applications I know:
Mulvey's proof of the Serre–Swan theorem in which he interprets the intuitionistically valid r …