Expansions of ordered fields without definable gaps

Mathematical Logic Quarterly 49 (1):72-82 (2003)

Abstract
In this paper we are concerned with definably, with or without parameters, complete expansions of ordered fields, i. e. those with no definable gaps. We present several axiomatizations, like being definably connected, in each of the two cases. As a corollary, when parameters are allowed, expansions of ordered fields are o-minimal if and only if all their definable subsets are finite disjoint unions of definably connected subsets. We pay attention to how simply a definable gap in an expansion is so. Next we prove that over parametrically definably complete expansions of ordered fields, all one-to-one definable continuous functions are monotone and open. Moreover, in both parameter and parameter-free cases again, definably complete expansions of ordered fields satisfy definable versions of the Heine-Borel and Extreme Value theorems and also Bounded Intersection Property for definable families of closed bounded subsets
Keywords definable extreme value theorem  definably connected  real closed  definable Heine‐Borel theorem  Definably complete  (weakly) o‐minimal  (definable) bounded intersection property  definable intermediate value property
Categories (categorize this paper)
DOI 10.1002/malq.200310005
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 47,122
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Noetherian Varieties in Definably Complete Structures.Tamara Servi - 2008 - Logic and Analysis 1 (3-4):187-204.
Splitting Definably Compact Groups in o-Minimal Structures.Marcello Mamino - 2011 - Journal of Symbolic Logic 76 (3):973 - 986.
Definably Complete Structures Are Not Pseudo-Enumerable.Antongiulio Fornasiero - 2011 - Archive for Mathematical Logic 50 (5-6):603-615.
Type-Definable and Invariant Groups in O-Minimal Structures.Jana Maříková - 2007 - Journal of Symbolic Logic 72 (1):67 - 80.
On Fields Definable inQ P.Anand Pillay - 1989 - Archive for Mathematical Logic 29 (1):1-7.
A Note on Weakly O-Minimal Structures and Definable Completeness.Alfred Dolich - 2007 - Notre Dame Journal of Formal Logic 48 (2):281-292.

Analytics

Added to PP index
2013-12-01

Total views
27 ( #349,270 of 2,289,298 )

Recent downloads (6 months)
12 ( #67,608 of 2,289,298 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature