# Tagged Questions

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### The composition of functors and algebraic structures

An algebraic structure can be viewed as a finite-product-preserving functor $X : \mathbf{L} \rightarrow \mathbf{C},$ where $\mathbf{L}$ is a Lawvere theory and $\mathbf{C}$ is a category. Thus given ...
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### Recommendation on a rigorous and deep introductory logic textbook

In this post, I don't mean any word by its somewhat "mathematical or logical" meaning but just "literally". It's been three years since I started "formal" mathematics, and now I'm familiar with set ...
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### How much does a theory tell about categorical properties of its models.

Let take a first order theory $T$ in a language $\mathcal L$. One can form the category $\mathrm{Mod}(T)$ whose objects are the models of $T$ (those $\mathcal L$-structures $\mathfrak M$ such that ...
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### Books/papers on model theory in non-monotonic logic

I am working on a project whose object language is in non-monotonic logic. Since the project involves reasoning about the models, I am thinking of translating a non-monotonic problem into a ...
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### Is there such a thing as (many-sorted) order-theoretic logic?

Many-sorted equational logic is a good option whenever we're interested in category-based semantics, like models in $\mathrm{Set}.$ However, its not so good if we're interested in $2$-poset-based ...
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### Online Model Theory Classes

Since "model theory" is kind of too general naming, I have encountered with lots of irrelevant results (like mathematical modelling etc.) when I searched for some videos on the special mathematical ...
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### Model theory in terms of type spaces/Lindenbaum algebras

Are there any good references that go into some detail of known 'translations' between properties of the type space of a model and the model theoretic properties of the model? All I seem to find are ...
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### The Logic of Satisfiability?

I am aware of some study into the logic of provability. It is generally taken to be intermediate in strength between S4 and S5 modal logics. Is there corresponding study into something like the logic ...
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### Model Theory and Topology Connections

I have studied a bit of model theory, when I say "a bit" I have studied much more than is available to a typical undergraduate in the UK (i think, certainly from what I have seen) but I am sure this ...
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### Gentle introduction into stability and classification theory

I am badly looking for a (very) gentle introduction into stability and classification theory answering at least some of the following questions: Why is a stable theory called "stable"? What is a ...
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### Learning Model Theory

What books/notes should one read to learn model theory? As I do not have much background in logic it would be ideal if such a reference does not assume much background in logic. Also, as I am ...
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### $\aleph_1$-categorical fields are algebraically closed.

I'd like to understand the proof that if $K$ is an infinite field the theory of $K$ is $\aleph_1$-categorical, then $K$ is algebraically closed--but I'm having trouble finding it in the literature. ...
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### number of linear orders

It is well known that for every infinite cardinal $\kappa$ the number of non-isomorphic total orders of cardinality $\kappa$ is $2^\kappa$. Who first proved this, and in what context? Was it proved ...
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### Structuralist slogans

I am afraid to make a bad impression by misusing this forum but I am looking for as-many-as-possible mathematically inspired formulations and references to one (sometimes vague) idea. The idea is ...
In Goldstern and Judah's The Incompleteness Phenomenon we are asked to prove that any model of the first two Peano Axioms: $$\forall x [Sx\neq0]$$ $$\forall x\forall y[Sx=Sy\implies x=y]$$ must be ...