The field of reals with a predicate for the real algebraic numbers and a predicate for the integer powers of two
type: Item
instance of: scholarly article
title: The field of reals with a predicate for the real algebraic numbers and a predicate for the integer powers of two
zbMATH Open document ID: 1341.03040
author: Mohsen Khani
published in: Archive for Mathematical Logic
publication date: 2015-11-18T00:00:00Z
review text: The paper studies properties of polynomially bounded o-minimal expansions of the field of real numbers. The author considers the theory of elementary dense pairs of models of such expansions. He proves that this theory is complete and axiomatises the field of real numbers with a predicate for the real algebraic numbers and a predicate for the integer powers of two. The author also describes types and definable sets of models of the theory and proves that this theory is dependent.
reviewed by: B. Sh. Kulpeshov
Mathematics Subject Classification ID: 03C10
Mathematics Subject Classification ID: 03C64
Mathematics Subject Classification ID: 12L12
zbMATH DE Number: 6511006
zbMATH Keywords: o-minimality
zbMATH Keywords: field of real numbers
zbMATH Keywords: dense pairs
zbMATH Keywords: integer powers of two
zbMATH Keywords: field of real algebraic numbers
MaRDI profile type: Publication
full work available at URL: s00153-015-0446-7
OpenAlex ID: W2199435462
cites work: Externally definable sets and dependent pairs
cites work: The field of reals with a predicate for the powers of two
cites work: Q3840696
cites work: Dimensions, matroids, and dense pairs of first-order structures
cites work: Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
cites work: Dependent pairs
cites work: Q4346720
cites work: Defining the set of integers in expansions of the real field by a closed discrete set
cites work: Q3837738
cites work: Q5700815
DOI: 10.1007/S00153-015-0446-7
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description: scientific article; zbMATH DE number 6511006