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A note on prime models in weakly o‐minimal structures
Author(s) -
Tari Somayyeh
Publication year - 2017
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201600029
Subject(s) - mathematics , prime (order theory) , uniqueness , extension (predicate logic) , decomposition , order (exchange) , property (philosophy) , combinatorics , pure mathematics , set (abstract data type) , discrete mathematics , mathematical analysis , computer science , biology , programming language , ecology , philosophy , finance , epistemology , economics
Let M = ( M , < , … ) be a weakly o‐minimal structure with the strong cell decomposition property. In this note, we show that the canonical o‐minimal extension M ¯ of M is the unique prime model of the full first order theory of M ¯ over any set A ⊆ M ¯ . We also show that if two weakly o‐minimal structures with the strong cell decomposition property are isomorphic then, their canonical o‐minimal extensions are isomorphic too. Finally, we show the uniqueness of the prime models in a complete weakly o‐minimal theory with prime models.