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A construction of real closed fields
Author(s) -
Tanaka Yuichi,
Tsuboi Akito
Publication year - 2015
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.201300052
Subject(s) - mathematics , algebraically closed field , extension (predicate logic) , integer (computer science) , field (mathematics) , analogy , pure mathematics , function (biology) , discrete mathematics , algebra over a field , computer science , linguistics , philosophy , evolutionary biology , biology , programming language
We introduce a new construction of real closed fields by using an elementary extension of an ordered field with an integer part satisfying PA . This method can be extend to a finite extension of an ordered field with an integer part satisfying PA . In general, a field obtained from our construction is either real closed or algebraically closed, so an analogy of Ostrowski's dichotomy holds. Moreover we investigate recursive saturation of an o‐minimal extension of a real closed field by finitely many function symbols.