Answer 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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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...
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