Expansions of subfields of the real field by a discrete set

Philipp Hieronymi. "Expansions of subfields of the real field by a discrete set." Fundamenta Mathematicae 215.2 (2011): 167-175. <http://eudml.org/doc/283210>.

@article{PhilippHieronymi2011,
abstract = {Let K be a subfield of the real field, D ⊆ K be a discrete set and f: Dⁿ → K be such that f(Dⁿ) is somewhere dense. Then (K,f) defines ℤ. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines ℤ. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire category theorem.},
author = {Philipp Hieronymi},
journal = {Fundamenta Mathematicae},
keywords = {defining the set of integers; discrete set; real field; expansions of subfields; cyclic multiplicative subgroups; definably complete expansion; Baire category theorem},
language = {eng},
number = {2},
pages = {167-175},
title = {Expansions of subfields of the real field by a discrete set},
url = {http://eudml.org/doc/283210},
volume = {215},
year = {2011},
}

TY - JOUR
AU - Philipp Hieronymi
TI - Expansions of subfields of the real field by a discrete set
JO - Fundamenta Mathematicae
PY - 2011
VL - 215
IS - 2
SP - 167
EP - 175
AB - Let K be a subfield of the real field, D ⊆ K be a discrete set and f: Dⁿ → K be such that f(Dⁿ) is somewhere dense. Then (K,f) defines ℤ. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines ℤ. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire category theorem.
LA - eng
KW - defining the set of integers; discrete set; real field; expansions of subfields; cyclic multiplicative subgroups; definably complete expansion; Baire category theorem
UR - http://eudml.org/doc/283210
ER -