A Note on Hieronymi’s Theorem: Every Definably Complete Structure Is Definably Baire

DOI10.1007/978-3-319-51718-6_15zbMath1436.03207OpenAlexW2621300800MaRDI QIDQ3298258

Antongiulio Fornasiero

Publication date: 14 July 2020

Published in: Groups, Modules, and Model Theory - Surveys and Recent Developments (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2158/1108498

zbMATH Keywords

Bairedefinably complete structure

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Model theory of ordered structures; o-minimality (03C64) Ordered fields (12J15)

Cites Work

• Relative Pfaffian closure for definably complete Baire structures
• Definably complete structures are not pseudo-enumerable
• Locally o-minimal structures and structures with locally o-minimal open core
• Expansions of o-minimal structures by iteration sequences
• A FUNDAMENTAL DICHOTOMY FOR DEFINABLY COMPLETE EXPANSIONS OF ORDERED FIELDS
• THE NON-AXIOMATIZABILITY OF O-MINIMALITY
• Definably complete Baire structures
• Definable versions of theorems by Kirszbraun and Helly
• Definably connected nonconnected sets
• A question of van den Dries and a theorem of Lipshitz and Robinson; Not everything is standard
• Structures having o-minimal open core
• Expansions of dense linear orders with the intermediate value property
• Theorems of the Complement
• An analogue of the Baire category theorem
• A first-order version of Pfaffian closure

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