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Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.

7 votes
Accepted

Is there a relationship between model theory and category theory?

Between model theory and category theory broadly conceived: not anything really compelling, because a category, on its own, does not stand as an interpretation for anything. Between model theory and …
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7 votes
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Weakest subsystems of second order arithmetic for mathematical logic

In fact, the incompleteness and completeness theorems can be proven in subsystems of second-order arithmetic weaker than RCA-0: incompleteness can be proven in EFA (first-order elementary arithmetic), …
Charles Stewart's user avatar
5 votes

Uses of bisimulation outside of computer science.

It's used in modal logic, where it was invented, and is used to define relations between models and constructions of new models from old models, which are used to show that different classes of model …
Charles Stewart's user avatar
2 votes

Models of ZFC Set Theory - Getting Started

From comment: how do we get from "the abstract" to "the concrete"? In my partly informed opinion, not by formal model theory! The ability of set theory to describe its own models is one of the pilla …
Charles Stewart's user avatar
3 votes
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Can infinite first-order categories be specified other than as categories of models?

Sure, by direct construction. Rings, preorders, the category of paths of a given graph, etc. But that's not what you wanted to know, is it?
Charles Stewart's user avatar
1 vote

What assumptions and methodology do metaproofs of logic theorems use and employ?

Certainly, classical logic is used in metalogic. I can't think, offhand, of any cases where I think its use is necessary. The methodology of reverse mathematics seems to offer a suitable, constructi …
Charles Stewart's user avatar