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Structure theorems for o-minimal expansions of groups

✍ Scribed by Mario J. Edmundo

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
169 KB
Volume
102
Category
Article
ISSN
0168-0072

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✦ Synopsis

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

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