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Unions and intersections of isomorphic images of nonstandard models of arithmetic. (English) Zbl 0621.03044

The author proves that any consistent extension T of first order Peano Arithmetic has a model \({\mathfrak M}^ s.\)t. there exists a family \(A_ k\) of densely ordered initial segments \({\mathfrak N}\) of \({\mathfrak M}\) with \({\mathfrak N}\leq {\mathfrak M}\) isomorphic to \({\mathfrak M}\) and a partition of \(A_ k\) into two sets \(A_ 1\), \(A_ 2\) such that \(\cap A_ 2=\cap A_ 1\). He uses methods of recursively-saturated-model theory and general theory of nonstandard models of arithmetic developed by Gaifman, Smorynski etc.
Reviewer: K.Potthoff

MSC:

03H15 Nonstandard models of arithmetic
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