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Results tagged with model-theory
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user 176424
Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.
3
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answers
89
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Realizing continuum many types and omitting one
I have a theory with finitely many relations, and would like to find a model of it with continuum-many 1-types realized, and one 2-type omitted. Is there a version of the Omitting Types Theorem that w …
- 429
0
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0
answers
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First-order logics expressively equivalent to the computable languages
There is a really nice theorem that the subsets of $(\Sigma^*, =_{el}, \preceq, (S_a)_{a \in \Sigma})$ definable in first-order logic are exactly the regular sets.
Where:
$\Sigma^*$ is the set of fin …
- 429
5
votes
1
answer
228
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What does the Ehrenfeucht-Fraïssé game on structures with infinitely many relations tell us?
EF-games are typically presented for structures with finitely many relations, and if you want to extend them to structures with functions, you can relationalize the functions. This seems to be to avoi …
- 429
7
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1
answer
241
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What is known about first order logic of $\mathbb{N}$ with + and a unary predicate?
In "Weak Second-Order Arithmetic and Finite Automata", Büchi claims that the first order theory of $\mathbb{N}$ with + and a predicate for recognizing powers of 2 ($Pw_2$) is expressively equivalent t …
- 429
2
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0
answers
99
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Name for the theory of words with equal length, prefix, successors
I've worked with this theory for a while, but I've never been quite sure what to call it:
$$(\Sigma^*, =_{el}, \preceq, (S_a)_{a \in \Sigma})$$
Where
$\Sigma^*$ is the set of finite words on finite a …
- 429