The real field with an irrational power function and a dense multiplicative subgroup

Details The real field with an irrational power function and a dense multiplicative subgroup The real field with an irrational power function and a dense multiplicative subgroup

2009-12-13

arxiv.org/abs/0912.2469v1

J. London Math. Soc. (2) 83 (2011) 153-16

Mathematics

Logic

Scientific paper

10.1112/jlms/jdq058

This paper provides a first example of a model theoretically well behaved structure consisting of a proper o-minimal expansion of the real field and a dense multiplicative subgroup of finite rank. Under certain Schanuel conditions, a quantifier elimination result will be shown for the real field with an irrational power function and a dense multiplicative subgroup of finite rank whose elements are algebraic over the field generated by the irrational power. Moreover, every open set definable in this structure is already definable in the reduct given by just the real field and the irrational power function.

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