All Questions
Tagged with model-theory reference-request
133
questions
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How to define $\Sigma \models \phi$ when $\phi$ is not a sentence? [duplicate]
Let $\Sigma$ be a theory and $\psi$ a sentence. I'm familiar with the notion of $\Sigma \models \psi$, however, lately, I've seen some authors using this notation when $\psi$ is a formula with free ...
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References for Maltsev's Theorem on $GL_n(F) \equiv GL_m(K)$ iff $K \equiv F$ and $m=n$.
I have recently found Maltsev's theorem: for $F$ and $K$ algebraically closed fields, $GL_n(F) \equiv GL_m(K)$ if and only if $K \equiv F$ and $m=n$ (thanks to this question: https://mathoverflow.net/...
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Has there been research on definability predicates, just like there has been research on truth predicates?
I know that there has been research on truth predicates, namely, formal theories of arithmetic with a truth predicate. You basically add a predicate $T$ to the language that models truth. I wonder, ...
- 21.5k
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Is it true but unassertable that there are undefinable real numbers?
I know of Joel David Hamkins's analysis of the so-called "math tea argument", namely that there are undefinable real numbers. Supposedly, he debunked this argument by constructing a ...
- 21.5k
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42
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Stronger version of proposition 1.1.8 in "Model theory" by Marker
In proposition 1.1.8 of "Model Theory: An Introduction" David Marker proves that:
If $\cal M$ is an $\cal L$-substructure of $\cal N$, $\bar a \in M$, and $\phi(\bar v)$ is a quantifier-...
- 4,962
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362
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Book recommendation for Model Theory
I want to start learning model theory for my master's thesis, but I can't find the right book for me. For some context, last year as an undergrad I had a class on logic where we learned the following: ...
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O-minimality and Putnam Competition [closed]
Someone told me that, on a recent Putnam exam, there was an A6 or B6 problem that could be solved using a recent result from o-minimality. Apparently this was not the intended solution method, but it ...
- 1,122
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Reference for Understanding Shelah's Proof of Vaught's Conjecture for $\omega$-stable Theories
I'm looking for a source to help me understand Shelah's proof of Vaught's Conjecture for $\omega$-stable Theories (https://shelah.logic.at/files/95409/158.pdf). An obvious candidate is Makkai's survey ...
- 1,569
2
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How to construct a homogeneous uncountable structure from a class of finitely generated structures
Fraïssé's famous result on homogeneous countable structures gives us a general method to contruct a countable homogeneous structure starting from the set of its finitely generated substructures. My ...
- 2,611
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124
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Is it possible to prove the absolute consistency of a theory by giving a finite model?
Most consistency results are relative, they say that if theory $T$ is consistent, then theory $T'$ is consistent. However, is it possible to prove the "absolute" consistency of a theory, by ...
- 21.5k
2
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What maps preserve and reflect basic Horn formulas?
A function $f : M \to N$ preserves and reflects a formula $\phi$ if $M \models \phi(\overline a) \iff N \models \phi(f(\overline a))$. For many fragments of first-order logic, there is a clear ...
- 7,290
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How are stable homogeneous structures interpreted in dense linear order?
In the report of this workshop, it is mentioned that every stable homogeneous structure is interpretable in the dense linear order. I failed to find this result in the papers cited in the report. Does ...
- 606
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Has numerosity-preserving functions between structures been studied before?
Isomorphisms are bijective functions between structures that preserve the constants, relations, and functions of the structure. I wonder, has a notion of "strong isomorphism" between ...
- 21.5k
4
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Modern exposition of Ramsey's famous paper "On a problem of formal logic"
I am interested in Ramsey's original motivation for proving the Ramsey theorem (on finding some set for which the coloring on its subsets are constant, for any given coloring of subsets). This link ...
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Stability theory in the context of $\omega$-stable theories
I'm looking for some references to get me started on stability theory. More specifically, I want to find sources that talk about notions in stability theory, but for $\omega$-stable theories, which ...
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