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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.

3 votes
Accepted

Is every cancellative semigroup a subdirect product of subdirectly irreducible cancellative ...

Sorry for answering my own question, but YCor's construction in a related thread (here) gave me a lightbulb moment. Hopefully, it's not a broken lightbulb. The answer to the question asked in the OP …
Salvo Tringali's user avatar
7 votes
2 answers
459 views

Is every cancellative semigroup a subdirect product of subdirectly irreducible cancellative ...

By a classical result of Birkhoff (that is, Theorem 2 in [G. Birkhoff, Subdirect unions in universal algebra, Bull. AMS, 1944]) and the trivial fact that the class of semigroups is closed under the ta …
Salvo Tringali's user avatar
1 vote
0 answers
194 views

Reference request: Models of isomorphic languages result into isomorphic categories

This is basically a reference request by someone who has not been educated as a logician and would like to be rigorous about certain preliminary aspects of model theory. Fix an uncountable universe $ …
Salvo Tringali's user avatar
4 votes
2 answers
1k views

Every abelian torsion-free group is strictly totally orderable (via the compactness theorem)

Let $\mathbb G = (G, +)$ be a group. We say that $\mathbb G$ is strictly totally orderable (others would say bi-orderable) if there exists a total order $\preceq$ on $G$ such that $x+z \prec y + z$ an …
Salvo Tringali's user avatar