Avoiding the projective hierarchy in expansions of the real field by sequences

DOI10.1090/S0002-9939-05-08112-8zbMath1093.03023MaRDI QIDQ3372135

Chris Miller

Publication date: 17 February 2006

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

o-minimalityfirst-order expansions of the field of real numbersinfinite discrete sets of real numbersinfinitely oscillating real functions

Mathematics Subject Classification ID

Rate of growth of functions, orders of infinity, slowly varying functions (26A12) Model theory of ordered structures; o-minimality (03C64)

Related Items

Expansions of o-minimal structures by dense independent sets ⋮ Defining additive subgroups of the reals from convex subsets ⋮ Expansions of the Real Field by Canonical Products ⋮ Defining the set of integers in expansions of the real field by a closed discrete set ⋮ Expansions of o-minimal structures by iteration sequences

Cites Work

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• Discrete "Orders of Infinity"
• A generalization of the Tarski-Seidenberg theorem, and some nondefinability results
• Growth Properties of Functions in Hardy Fields
• The real field with convergent generalized power series
• Exponentiation is Hard to Avoid
• Quasianalytic Denjoy-Carleman classes and o-minimality
• Pfaffian differential equations over exponential o-minimal structures
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