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Structure theorems for o-minimal expansions of groups
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Orientador(es)
Resumo(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,+).
Descrição
Palavras-chave
O-minimal structures Structure theorems
Contexto Educativo
Citação
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
Editora
Elsevier