Expansions of ordered fields without definable gaps

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

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

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
2013-12-01

Downloads
31 (#445,254)

6 months
3 (#445,838)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Generalizing theorems in real closed fields.Matthias Baaz & Richard Zach - 1995 - Annals of Pure and Applied Logic 75 (1-2):3-23.
An open mapping theorem for o-minimal structures.Joseph Johns - 2001 - Journal of Symbolic Logic 66 (4):1817-1820.

Add more references