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Results tagged with model-theory
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user 3154
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
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), …
- 2,283
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 …
- 2,283
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 …
- 2,283
3
votes
Accepted
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?
- 2,283
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 …
- 2,283
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 …
- 2,283