# Tagged Questions

Model theory is the study of (classes of) mathematical structures (e.g. groups, fields, graphs, universes of set theory) using tools from mathematical logic. Objects of study in model theory are models for formal languages which are structures that give meaning to the sentences of these formal ...

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### How it can be formally proved that a formula of First Order Logic with identity has only infinite models?

I have an irreflexive and transitive relation $R$. Then I want to prove that $\forall x \exists y (xRy)$ has only infinite models. I have an intuitive idea for which the relation $R$ cannot be ...
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### What's the difference between a model and a $\sigma$ structure?

In model theory, I haven't actually seen the word "model" defined. The only thing I've seen defined is a $\sigma$ structure for some signature $\sigma$. I read phrases like $A$ is a model of some ...
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### Infinite, finite and arbitrarily large models.

How is it possible to have a sentence of First Order Logic with identity such that it has both finite and infinite models, but not arbitrarily large models? Edited: (arbitrarily large -finite- ...
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### First order theories, interpretation, concrete example, proof

I read a proof that no model of a certain f.o. theory $T_1$ is definable in $(Q,<)$ and I have a problem with understanding the very end of Lemma 3.2 here. "The distance from $\alpha_i$ to ...
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### Ultraproduct, axiomatizability,models,finite structures,language of one biary symbol

If we know that first order axiomatizable theories have classes of models in one binary relational symbol $R$,say, closed under ultraproducts, how can I see that finite graphs, i.e. finite models in ...
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### Principia Mathematica Part VI “Quantity” vs Part IV “Relation Arithmetic”

In "My Philosophical Development", of Principia Mathematica Part IV "Relation Arithmetic", Bertrand Russell laments: "I think relation-arithmetic important, not only as an interesting ...
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### Model Theory - exercise [closed]

I'm trying to understand model theory without much mathematical background. I need an example of how to do exercises in model theory. Could you please explain to me for instance how to resolve the ...
The theory $Th_{\exp,\mathrm{fields}}$ of exponential ordered fields is the first-order theory over $\left\langle +,\cdot,0,1,<,\exp\right\rangle$ whose axioms state that the model is an ordered ...