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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.

5 votes

Is the ultraproduct concept fundamentally category-theoretic?

There are already several answers describing how ultraproducts arise naturally from categorical considerations. However, I don't think any of them address this part of the question: I would be very i …
varkor's user avatar
  • 10.7k
8 votes

Comparing the existing formulations of universal algebra and their levels of generality

fosco gives a good overview of the general theory in their answer. I would like to point out two different generalisations of algebraic theory that are not, as far as I am aware, subsumed by any of th …
varkor's user avatar
  • 10.7k