Expansions of subfields of the real field by a discrete set

• Autorzy: Philipp Hieronymi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54E52: Baire category, Baire spaces
• 03C64: Model theory of ordered structures; o-minimality
• 14P10: Semialgebraic sets and related spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 215
• Numer: 2
• Strony: 167-175

Daty

wydano

2011

Twórcy

autor

Philipp Hieronymi

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

Identyfikatory

DOI

10.4064/fm215-2-4