Structure theorems for o-minimal expansions of groups

Edmundo, Mário Jorge

http://hdl.handle.net/10400.2/2755

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
st.pdf		215.88 KB	Adobe PDF	Download

Send Feedback

Authors

Edmundo, Mário Jorge

Abstract(s)

Let R be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) R is semi-bounded, (2) R has no poles, (3) R cannot define a real closed field with domain R and order <, (4) R is eventually linear and (5) every R-definable set is a finite union of cones. As a corollary we get that Th(R) has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations, bounded R-definable sets and a symbol for each definable endomorphism of the group (R,0,+).

Keywords

O-minimal structures Structure theorems

URI

http://hdl.handle.net/10400.2/2755

Citation

Edmundo, Mário Jorge - Structure theorems for o-minimal expansions of groups. "Annals of Pure and Applied Logic" [Em linha]. ISSN 0168-0072. Vol. 102, Nº 1-2 (Mar. 2000), p. 1-30