A construction of real closed fields | Zendy

Tanaka Yuichi | Zendy; Tsuboi Akito | Zendy

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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.

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