Ignjatović, Aleksandar Unions and intersections of isomorphic images of nonstandard models of arithmetic. (English) Zbl 0621.03044 Publ. Inst. Math., Nouv. Sér. 39(53), 25-28 (1986). 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 Keywords:non-standard models of Peano Arithmetic; initial segments PDFBibTeX XMLCite \textit{A. Ignjatović}, Publ. Inst. Math., Nouv. Sér. 39(53), 25--28 (1986; Zbl 0621.03044) Full Text: EuDML