# 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.

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### Is there difference in notion of measurability in classical versus constructive?

Are there notions of measure and examples of sets measurable in that measure in classical logic but not in constructive logic (I think there cannot be counterexamples in other direction)? Are there ...
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### Saturated differentially closed field

What means "saturated" in "saturated diff erentially closed field" ?
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### What is a good definition of a mathematical structure?

At the moment I am writing a textbook in Foundations of Mathematics for students and trying to give a precise definition of a mathematical structure, which is the principal notion of structuralist ...
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### Topological Vaught's conjecture for special theories

As is know, Vaught's conjecture is a special case of topological Vaught's conjecture. On the other hand, the Vaught's conjecture is true for the following theories: 1- $\omega$-stable theories (...
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### Results of geometric model theory

I read in some places that model theory has useful applications in algebraic geometry. Could someone give me some results that come from applying model theory to algebraic geometry? I also saw that ...
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### Where is the flaw in this argument with $p$-adic extensions?

I cannot find what I am missing in the following computation. Let $K=\mathbb{Q}_p(p^{1/{(p-1)p^{\infty}}})$ and $L=\mathbb{Q}_p(\zeta_{p^{\infty}})$, where $\zeta_{p^n}$ is a primitive $p^n$-th root ...
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### What does second order set theory give us that is new?

There is a natural analogy between the theories PA and ZFC. See the linked question by Gro-Tsen here. Peano arithmetic (PA) is a first order approximation to the natural numbers. As is well known, ...
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### The “contrary” of an isomorphism

Roughly, my question is: is there a standard name for functions which one might characterise as the "contrary" of an isomorphism? Here is a more precise version of my question. Working model-...
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### Compatible and incompatible sets [closed]

Definition of the compatibility relation I have defined a relation $\mathsf{C}$ for sets that captures (to some extent) the notion of compatibility. In order to do this, we need an operation \$': \...
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### Is the union of a chain of elementary embeddings elementary?

I am a little confused about what I think must be either a standard theorem or a standard counterexample in model theory, and I am hoping that the MathOverflow model theorists can help sort me out ...
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### Is the equational theory of groups axiomatized by the associative law?

Consider the class of groups in the signature {*}. Is the equational theory of that class axiomatized by the associative law? I asked this on math stack exchange but I didn't receive a satisfactory ...
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### Survey article model theory research

I've taken a graduate course in model theory and I like it so much that I can imagine doing research in this area. Are there survey articles or review papers on the current research topics in model ...