Answer by Alex Kruckman for Elementary embedding and infinite atomic Boolean...
Noah's answer is correct: an embedding of atomic Boolean algebras which preserves the atoms is an elementary embedding. Let me give a few more details.The theory of atomic Boolean algebras, when...
View ArticleAnswer by Noah Schweber for Elementary embedding and infinite atomic Boolean...
A useful idea for this sort of problem is to look for quantifier elimination, if not in the original language then at least in some "not-too-great" enlargement of it. And indeed this works here.Augment...
View ArticleElementary embedding and infinite atomic Boolean algebras
Let $A$ and $B$ be two infinite atomic Boolean algebras with a monomorphism $h: A \rightarrow B$ that embeds $A$ into $B$. Also, let it be such that for any atom $a \in A$, $h(a)$ is an atom in $B$.Let...
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