Elementary epimorphisms between models of set theory
نویسندگان
چکیده
We show that every Π1-elementary epimorphism between models of ZF is an isomorphism. On the other hand, nonisomorphic Σ1-elementary epimorphisms between models of ZF can be constructed, as can fully elementary epimorphisms between models of ZFC−. Elementary epimorphisms were introduced by Philipp Rothmaler in [Rot05]. A surjective homomorphism f : M → N between two model-theoretic structures is an elementary epimorphism if and only if every formula with parameters satisfied by N is satisfied in M using a preimage of those parameters.
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ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 55 شماره
صفحات -
تاریخ انتشار 2016