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Results tagged with lo.logic
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user 152679
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.
3
votes
Accepted
"Tietze-like transformations" for defining interesting bijections between algebraic structures
Tietze transformations for arbitrary algebraic theories (with respect to their presentations) have been considered in Malbos–Mimram's Homological Computations for Term Rewriting Systems, in the contex …
- 10.7k
4
votes
Categorical semantics of universe levels in dependent type theory
A universe in a category with display maps is a specified display map $\tilde U \to U$ (cf. Section 5.5 of Taylor's thesis Recursive Domains, Indexed Category Theory and Polymorphism, or Section 9.6 o …
- 10.7k
9
votes
1
answer
301
views
Internal logic of locally strongly finitely presentable categories
There is a duality between locally strongly finitely presentable (LSFP) categories and (Cauchy complete) cartesian categories, i.e. multisorted algebraic theories [1]. The internal logic of cartesian …
- 10.7k
5
votes
Is the ultraproduct concept fundamentally category-theoretic?
There are already several answers describing how ultraproducts arise naturally from categorical considerations. However, I don't think any of them address this part of the question:
I would be very i …
- 10.7k
8
votes
Comparing the existing formulations of universal algebra and their levels of generality
fosco gives a good overview of the general theory in their answer. I would like to point out two different generalisations of algebraic theory that are not, as far as I am aware, subsumed by any of th …
- 10.7k