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Results tagged with model-theory
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user 16537
Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.
4
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answers
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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 …
- 10.5k
1
vote
0
answers
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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 $ …
- 10.5k
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 …
- 10.5k
7
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2
answers
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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 …
- 10.5k