Geodesic
Expansions of subfields of the real field by a discrete set
Philipp Hieronymi1
1 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801, U.S.A.
Fundamenta Mathematicae, Tome 215 (2011) no. 2, pp. 167-175

Voir la notice de l'article provenant de 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.
DOI : 10.4064/fm215-2-4
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

Philipp Hieronymi 1

1 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801, U.S.A. 
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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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