Questions tagged [model-theory]
Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.
1,228
questions
1
vote
0
answers
206
views
Interpretation of model theory in algebraic geometry
I found a paper Some applications of a model theoretic fact to (semi-) algebraic geometry by Lou van den Dries. In this paper, the author uses model theoretical methods to prove the completeness of ...
- 227
9
votes
2
answers
1k
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 ...
- 5,038
0
votes
0
answers
129
views
Provability predicates
We know that there are provability predicates, that is, predicates derived from the recursive relation "x is a demonstration of y", with which Godel's second incompleteness theorem would not ...
- 265
4
votes
0
answers
281
views
Which countable sets don't drastically change the definable topologies on $\mathbb{R}$?
For $\mathcal{M}$ an expansion of $\mathcal{R}=(\mathbb{R};+,\times)$ and $A\subseteq\mathbb{R}$, let $\tau^\mathcal{M}_A$ be the topology on $\mathbb{R}$ generated by the sets definable in $\mathcal{...
- 20.7k
11
votes
1
answer
665
views
On the classification of second-countable Stone spaces
Let $X$ be a Stone space (i.e. totally disconnected compact Hausdorff). Then the following are equivalent:
$X$ is second countable
$X$ is metrizable
$X$ has countably many clopen subsets
$X$ is an ...
- 62.6k
4
votes
1
answer
486
views
Truth Values of Statements in non-standard models
Excuse me, if the question sounds too naive.
Non-standard models of PA will have statements of non-standard lengths, basically infinite. And it is also true that every statement of a theory will have ...
- 1
3
votes
0
answers
140
views
Lindström's theorem part 2 for non-relativizing logics
By "logic" I mean the definition gotten by removing the relativization property from "regular logic" — see e.g. Ebbinghaus/Flum/Thomas — and adding the condition that for every ...
- 20.7k
8
votes
1
answer
1k
views
Worst of both worlds?
It's well known that $\mathsf{AC}$ implies the existence of non-measurable sets. And it's also true that, if all sets are measurable, then $|\mathbb{R}/\mathbb{Q}| > |\mathbb{R}|$. But is there a ...
- 309
0
votes
0
answers
104
views
Can a definable group of definable automorphisms of a field contain the Frobenius automorphism?
Let $K$ be an infinite definable field of characteristic $p >0$ in a certain theory $T$ with a definable group of definable automorphisms. Can this group contain the Frobenius automorphism?
- 1
2
votes
0
answers
495
views
Gödel's second incompleteness theorem [closed]
Apparently, see Feferman or Wikipedia, in a consistent system there are formulations of consistency that are demonstrable in the system itself while others are not. What distinguishes one from another?...
- 265
6
votes
1
answer
310
views
Original motivations of Fraïssé's amalgamation construction
Roland Fraïssé introduced in the 50's his famous construction of Fraïssé limits, and then Ehud Hrushowski modified it in the early 90's to construct new structures.
The motivations for the latter was ...
- 1,005
11
votes
1
answer
436
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
3
votes
1
answer
99
views
Is the filter generated by $A$-generic sets S1-prime?
Let $\mathfrak U$ be a monster model.
Let $A\subseteq\mathfrak U$ be a small set of parameters.
A set $\mathfrak D\subseteq\mathfrak U^{|x|}$ is $A$-generic if finitely many translations of $\mathfrak ...
2
votes
1
answer
557
views
Logical content of Gauss's Lemma (arithmetic)
In the context where $a$, $b$, $c$ are integers we have $(a \mid bc, a\land b = 1) \Rightarrow a\mid c$. This result is called Gauss's Lemma in French Highschool.
It is well known that (Steve Awodey, ...
- 29
5
votes
0
answers
227
views
Classical first-order model theory via hyperdoctrines
I have been reading this discussion by John Baez and Michael Weiss and I find this approach to model theory using boolean hyper-doctrines very interesting. One of their goal was to arrive at a proof ...
- 3,084