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Results tagged with lo.logic
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user 14969
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.
29
votes
6
answers
4k
views
Concrete example of $\infty$-categories
I've seen many different notions of $\infty$-categories: actually I've seen the operadic-globular ones of Batanin and Leinster, and the opetopic, and eventually I'll see the simplicial ones too. Altho …
- 3,349
14
votes
3
answers
2k
views
Differences between logic with and without equality
By logic without equality I mean those kind of logics where equality is treated as a binary relation satisfying some axioms, as opposed to a logics where equality is a logical symbol satisfying some i …
- 3,349
9
votes
How do we construct the Gödel’s sentence in Martin-Löf type theory?
I am a little bit rusty on the subject so I hope whatever I am going to say is correct (otherwise someone else will possibly correct me and I'll learn something :) ).
Before I start allow me to stres …
- 3,349
8
votes
4
answers
958
views
Higher categories in logic
I've read somewhere (probably in the nlab) that higher category theory has application in logic.
By the way since now the only applications of higher category theory I've seen are in homotopy theory a …
- 3,349
6
votes
The groupoid of algebraic expressions and proofs
The construction you describe seems more like the the category of reductions generated by the abstract rewrite system given by an algebraic theory.
I suggest you take a look to section 8.2("Rewrite s …
- 3,349
6
votes
Category theorists stance on deductive systems
I think the idea should pretty much like this: once you drop the requirement for the deductive system to be freely generated from the axioms by the inference rules (i.e. you accept the existence of no …
- 3,349
5
votes
Circular, or missing, definition in set theory?
If by "the domain of $x \in A$" you mean the objects you can put in $x$ and $A$ then the answer is everything.
This is due to the fact that in set theories such as ZFC and NBG all objects are set/clas …
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3
votes
1
answer
133
views
Internal equality for Eq-fibrations' morphisms
I have posted this question here on M.SE but since it received little attention and since it seems difficult to find helpfule references I reposting it here.
In Jacob's Categorical logic and Type The …
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3
votes
Accepted
What is the relationship between FOPL and Higher Order Logics?
As François G. Dorais pointed out you have to read carefully wikipedia's article.
The main difference in expressiveness between first order logic and second order logic is given by the semantics.
…
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3
votes
2
answers
627
views
Further relation between monads and theories
This question want to be a follow up of the following question.
In that thread I was interested in understanding relation between various presentation of algebraic theories. In particular in Eduardo P …
- 3,349
2
votes
Is PA consistent? do we know it?
I'd been very interested in foundational questions for a long time so I think I can say something about it. To understand the question I think it is necessary make some comment: mathematical logic is …
1
vote
Accepted
Is there a precise definition of "mathematical formula"?
Every book of mathematical logic should be a good reference where to find the notion of formula.
Usually when one refers to formulas it means formulas of a first order language.
A first order langua …
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0
votes
Large categories vs. $\mathrm{U}$-categories: why is the loss of category-theoretic informat...
I think there can be no easy answer to your question or to be exact I'm afraid that there are many different reasons for using universes instead of sticking with just one foundational set theory.
I w …
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