# Tagged Questions

**0**

votes

**0**answers

95 views

### How to prove a Lefschetzesque principle for relative homology and absolute homology

Here is my conjecture:
If H is some homology theory from some abelian category A to some abelian category B, E is the class of all epimorphism in A, E' is some closed class of epimorphisms in A and ...

**2**

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**0**answers

100 views

### Is the following a sufficient condition for being a primal algebra?

I have a question regarding universal algebra and, in particular, primal algebras:
Suppose that A is a finite simple algebra with no proper subalgebra, no automorphism except the identity map, with a ...

**1**

vote

**1**answer

135 views

### How can one define the direct limit of classes?

If we have a family of classes $(\mathfrak{M}_\alpha)_{\alpha\in D}$ of $\in$-structures with $D$ being a limit ordinal or the class of ordinals, and a family ...

**2**

votes

**0**answers

115 views

### Preimages of accessible full subcategories

My question is ultimately about the model theory of $L_{\infty, \omega}$, but it is more convenient to phrase it in terms of category theory. Suppose I have finitely accessible categories ...

**3**

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**0**answers

144 views

### Equational theories determined by “identities without variables”

How to characterize equational theories $T$ which have the following property: for any two terms $t(x_1,...,x_n)$ and $t'(x_1,...,x_n)$ in the signature of $T$, if for any closed terms (i. e. terms ...

**13**

votes

**3**answers

450 views

### Varieties where every algebra is free

I'd like to know more about varieties (in the sense of universal algebra) where every algebra is free. Another way to state the condition is that the comparison functor from the Kleisli category to ...

**12**

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**3**answers

591 views

### The interplay between certain aspects of interpretability, model theory and category theory

I have some questions about the interplay of interpretability, model theory and category theory. Since I had difficulties in finding literature or other helpful information about this topic, it would ...

**7**

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**0**answers

188 views

### Is there a Rado category?

The Rado graph appears to have a nice universality property (it contains all finite and all countably infinite graphs as induced subgraphs) and homogeinety property (any isomorphism between ...

**4**

votes

**1**answer

141 views

### Sketches for categories of models of complete theories

In Accessible categories : the foundations of categorical model theory, chapter 3 p.58, Makkai and Paré claim that there is "an (obvious) identification of a class of sketches so that the categories ...

**3**

votes

**1**answer

168 views

### Completeness theorem via syntactic categories

The nLab says in its internal logic article that the Completeness Theorem can be proven via a ``generic model'' of the theory. The model is generic in the sense that the only things true of it are ...

**6**

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**0**answers

228 views

### Is there Ultracoproduct-like construction for topological spaces in general?

In
http://arxiv.org/pdf/math/9704205.pdf
they define the ultracoproduct of a sequence of compact Hausdorff spaces, $\sum_\mathcal{U}X_i$ along an ultrafilter $\mathcal{U}$ as the Wallman-Frink ...

**3**

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**0**answers

160 views

### Is there a useful Galois connection between Languages and Grammars?

I've just beginning to learn logic and proof theory - and the following rather vague and perhaps ill-formed question occurred to me.
Given an alphabet it's straightforward to construct the Language, ...

**3**

votes

**1**answer

351 views

### Interpretations as morphisms

Model-theoretic interpretations seem to give rise to categories in which morphisms are not functions. To name just two small examples:
the category of finite graphs with interpretations between them
...

**3**

votes

**2**answers

334 views

### The category of Boolean-valued models associated to a model of ZFC

This is related to my previous question here, and indirectly motivated by Andreas Blass intriguing answer therein:
start from a ZF transitive model $M$, and consider the category $CBA(M)$ of ...

**1**

vote

**1**answer

405 views

### A Dedekind (pseudo) finite set

Quoting the wiki:- a set A is Dedekind-infinite if some proper subset B of A is equinumerous to A. Explicitly, this means that there is a bijective function from A onto some proper subset B of A. -.
...

**7**

votes

**1**answer

572 views

### 2nd Incompleteness and Model Theory

In the presence of Godel's Completeness Theorem, the 2nd Incompleteness Theorem has
the following strictly model theoretic interpretation: if there exists any model at all of (say) ZFC, there also ...

**6**

votes

**3**answers

1k views

### Formalizing “no junk, no confusion”

Goguen has popularized the initial algebra view of semantics via his "no junk, no confusion" slogan. By "no junk", he means that models of a theory presentation should not have unnecessary elements, ...

**0**

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**1**answer

448 views

### Is theory with domain of interpretation in second order objects a First Order Theory?

Thank everybody for answering my previous questions: first, and second.
Here I would like to ask about some important thing which I do not understand clearly.
Is it necessary for theory to have ...

**11**

votes

**1**answer

644 views

### How are the two natural ways to define ''the category of models of a first-order theory T'' related?

Background/Motivation: Inspired by an interesting question by Joel, I've been wondering about the relationship between two very natural ways to define the category of ''all models of T'' where T is a ...

**11**

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**4**answers

2k views

### Category theory and model theory as “natural” counterparts

I am aware of the profound discussion of the relationship between category theory and model theory (e.g. at The n-Category Café) but do wonder why category theory (CT) is not opposed to model theory ...

**12**

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**3**answers

829 views

### Can we recognize when a category is equivalent to the category of models of a first order theory?

Many of the most canonical early examples of categories
arise as the collection of models of a fixed first order
theory, with the related model-theoretic concept of
homomorphism. For example, the ...

**2**

votes

**4**answers

465 views

### Category of groups = Category of models of group theory?

Is the category of groups with group-homomorphisms the same as the category of models of group theory with elementary maps?
If not so: why?

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vote

**3**answers

336 views

### Can infinite first-order categories be specified other than as categories of models?

I am glad to see that a general question like Is there a relationship between model theory and category theory? receives quite a lot attention and no down-votes for being too general and unspecific. ...

**10**

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**5**answers

2k views

### Is there a relationship between model theory and category theory?

According to Chang and Keisler's "Model Theory", Model Theory = Universal Algebra + Logic. Model theory generalized Universal Algebra in the sense that we allow relation while in Universal Algebra we ...

**31**

votes

**7**answers

2k views

### Is the ultraproduct concept fundamentally category-theoretic?

Once again, I would like to take advantage of the large number of knowledgable category theorists on this site for a question I have about category-theoretic aspects of a fundamental logic concept.
...