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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Classification of properties of structures
Is there a sensible classification of the properties of structures with a given signature $\sigma$, e.g. graphs with $\sigma = \lbrace R \rbrace$?
For example like this:
properties defined by first-...
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Isomorphism types or structure theory for nonstandard analysis
My question is about nonstandard analysis, and the diverse possibilities for the choice of the nonstandard model R*. Although one hears talk of the nonstandard reals R*, there are of course many non-...
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What are some results in mathematics that have snappy proofs using model theory?
I am preparing to teach a short course on "applied model theory" at UGA this summer. To draw people in, I am looking to create a BIG LIST of results in mathematics that have nice proofs ...
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In model theory, does compactness easily imply completeness?
Recall the two following fundamental theorems of mathematical logic:
Completeness Theorem: A theory T is syntactically consistent -- i.e., for no statement P can the statement "P and (not P)" be ...
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Countable atomless boolean algebra covered by a larger boolean algebra
Suppose $Q$ is an atomless countable boolean algebra, and $B$ is an arbitrary atomless boolean algebra. $Q$ is unique modulo isomorphisms. There is a subalgebra in $B$ that is isomorphic to $Q$. There ...
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Is the theory of incidence geometry complete?
Consider the basic axioms of planar incidence geometry, which allow us to speak of in-betweeness, collinearity and concurrency. These axioms per se are not complete, since for example, Desargues ...
user2529
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What assumptions and methodology do metaproofs of logic theorems use and employ?
In logic modules, theorems like Soundness and completeness of first order logic are proved. Later, Godel's incompleteness theorem is proved. May I ask what are assumed at the metalevel to prove such ...
user2529
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Elementary theory of finite fields
I read on Ax's article that the elementary theory of finite fields is decidable if one assumes the continuum hypothesis to be true. What about if one assumes the hypothesis to be false?
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nonstandard set theories
Does anyone know of good references for nonstandard set theories and their applications to various branches of mathematics like category theory, algebra, geometry, etc.?
Edit: What I mean by "...
user577
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A few questions on model theory, especially model theory of rings
I have never really read anything proper about model theory, so I have a few questions:
Someone told me that a school of logicians managed to give a very short proof of Falting's Theorem using model ...
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Intuitionistic Lowenheim-Skolem?
Is there a version of the Löwenheim-Skolem theorem in intuitionistic logic? I'm particularly interested in the "downward" form. The standard proof I know uses the Tarski-Vaught test for ...
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Actions of finite permutation groups on hereditarily finite sets.
Model theorists have a lot to say about so-called definable imaginary elements of a structure. One way to formulate imaginaries is the following: Suppose $\mathcal{M}$ is a structure with universe $M$,...
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Complete theory with exactly n countable models?
For $n$ an integer greater than $2$, Can one always get a complete theory over a finite language with exactly $n$ models (up to isomorphism)?
There’s a theorem that says that $2$ is impossible.
My ...
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