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Is Hodges' definition of elementary embedding wrong?
I am reading the beautiful book by Hodges, A Shorter Model Theory. In sections 2.4 and 2.5 the authors classifies formulas through maps which preserve them and viceversa. All is very clear, except from...
View ArticleAnswer by Olivier Roche for Is Hodges' definition of elementary embedding wrong?
This $\Longrightarrow$ implies the desired $\Longleftrightarrow$. It would indeed make more sense to define an elementary embedding $f$ to be a map $f : A \mapsto B$ satisfying $\forall \phi \ \forall...
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