Expansions of subfields of the real field by a discrete set
Fundamenta Mathematicae, Tome 215 (2011) no. 2, pp. 167-175
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
Let $K$ be a subfield of the real field,
$D\subseteq K$ be a discrete set and $f:D^n \to K$ be such that $f(D^n)$ is somewhere dense. Then $(K,f)$ defines $\mathbb{Z}$. We present several applications of this result. We show that $K$ expanded by predicates for different cyclic multiplicative subgroups defines $\mathbb Z$. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire category theorem.
Keywords:
subfield real field subseteq discrete set somewhere dense defines mathbb present several applications result expanded predicates different cyclic multiplicative subgroups defines mathbb moreover prove every definably complete expansion subfield real field satisfies analogue baire category theorem
Affiliations des auteurs :
Philipp Hieronymi 1
@article{10_4064_fm215_2_4,
author = {Philipp Hieronymi},
title = {Expansions of subfields of the real field by a discrete set},
journal = {Fundamenta Mathematicae},
pages = {167--175},
year = {2011},
volume = {215},
number = {2},
doi = {10.4064/fm215-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm215-2-4/}
}
Philipp Hieronymi. Expansions of subfields of the real field by a discrete set. Fundamenta Mathematicae, Tome 215 (2011) no. 2, pp. 167-175. doi: 10.4064/fm215-2-4
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