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Results tagged with lattice-theory
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user 11640
The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
8
votes
Accepted
Posets (partially ordered sets) in equational logic
No. The category of models of an equational theory (i.e. a variety in the sense of universal algebra) is always a regular category, but the category of posets is not regular.
- 15.9k
23
votes
1
answer
962
views
Are there axioms satisfied in commutative rings and distributive lattices but not satisfied ...
Consider the language of rigs (also called semirings): it has constants $0$ and $1$ and binary operations $+$ and $\times$. The theory of commutative rigs is generated by the usual axioms: $+$ is asso …
- 15.9k
7
votes
1
answer
125
views
Universally closed implies proper for locales
It is well known that:
Theorem.
For a locale (resp. topological space) $X$, the following are equivalent:
$X$ is compact, i.e. every open cover of $X$ has a finite subcover.
For every locale (resp. …
- 15.9k
2
votes
Universally closed implies proper for locales
It turns out that Vermeulen has essentially answered the question in [A note on stably closed maps of locales].
The argument there implies:
Theorem.
Let $g : X \to S$ be a morphism of locales.
The fol …
- 15.9k