All Questions
Tagged with topos-theory model-theory
11 questions
9
votes
2
answers
2k
views
Truth in a different universe of sets?
I understand that provability and truth as different concepts.
Provability is syntactic, it only concerns whether the given
sentence can be derived by reiterating the inference rules over a
collection ...
- 5,230
11
votes
1
answer
461
views
Are flat functors out of a finite category necessarily finite?
Note: I've originally asked this question on math stack exchange, but I have learnt that this is the better place to ask for research level questions, so I have deleted the original question there.
...
- 113
17
votes
3
answers
2k
views
Recommendations to learn about the use of toposes in logic?
I'd like to learn about the use of toposes in logic. The "logic" side I know quite well, but of the "topos" side I am totally ignorant.
Which books/articles (formal and/or casual) ...
- 1,031
9
votes
2
answers
2k
views
Are the models of infinitesimal analysis (philosophically) circular?
Infinitesimal analysis (by which I mean that originating from topos theory---not the nonstandard analysis of Robinson) seeks to recover the pre-limit notions of calculus (which are sufficiently useful ...
- 341
6
votes
1
answer
430
views
Joyal arithmetic universes and the Box operator
Last month @godelian, alias Christian Espíndola, in a FOM post has mentioned Joyal's proof of Godel's second incompleteness via the so-called Arithmetic Universes, introduced by Joyal around 1973, ...
- 7,853
10
votes
0
answers
267
views
Classifying cohomology
In his 1973 topos seminar in Buffalo (the tapes are now freely available online!), Grothendieck said:
The cohomology of a topos associated to an algebraic structure should be called the "...
- 133
13
votes
1
answer
1k
views
Model existence theorem in topos theory
One of most classical and somehow striking result in classical model theory states:
A consistent first order theory $T$ has a model.
Few considerations are needed.
This result is not true for ...
- 9,111
26
votes
2
answers
2k
views
Precise relationship between elementary and Grothendieck toposes?
Elementary toposes form an elementary class in that they are axiomatizable by (finitary) first-order sentences in the "language of categories" (consisting of a sort for objects, a sort for morphisms, ...
user71137
2
votes
0
answers
392
views
Geometric Theories have models in any Grothendieck Topos?
This question is linked to this one.
My question is:
Is it true any consistent geometric (here I mean coherent theory, different books have different standards) theory $T$ has a model in a ...
- 9,111
23
votes
1
answer
2k
views
Variant of Conceptual Completeness
Let $\mathcal{C}$ and $\mathcal{D}$ be pretopoi, and let $f: \mathcal{C} \rightarrow \mathcal{D}$ be a pretopos functor (that is, a functor which preserves finite coproducts, finite limits, and ...
- 17.8k
7
votes
1
answer
776
views
2nd Incompleteness and Model Theory
In the presence of Godel's Completeness Theorem, the 2nd Incompleteness Theorem has
the following strictly model theoretic interpretation: if there exists any model at all of (say) ZFC, there also ...
- 17.6k