A FUNDAMENTAL DICHOTOMY FOR DEFINABLY COMPLETE EXPANSIONS OF ORDERED FIELDS

DOI10.1017/jsl.2014.10zbMath1373.03062arXiv1305.4767OpenAlexW1549663977MaRDI QIDQ2795910

Antongiulio Fornasiero, Philipp Hieronymi

Publication date: 22 March 2016

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4767

zbMATH Keywords

second-order arithmeticLebesgue's differentiation theoremdefinably complete expansion

Mathematics Subject Classification ID

Model theory of ordered structures; o-minimality (03C64) Ordered fields (12J15)

Related Items (4)

The surjectivity and the continuity of definable functions in some definably complete locally o-minimal expansions and the Grothendieck ring of almost o-minimal structures ⋮ A Note on Hieronymi’s Theorem: Every Definably Complete Structure Is Definably Baire ⋮ PSEUDO-FINITE SETS, PSEUDO-O-MINIMALITY ⋮ D-minimal expansions of the real field have the zero set property

Cites Work

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• Definably complete structures are not pseudo-enumerable
• Locally o-minimal structures and structures with locally o-minimal open core
• Definably complete Baire structures
• Expansions of subfields of the real field by a discrete set
• Defining the set of integers in expansions of the real field by a closed discrete set

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