When is scalar multiplication decidable?

Philipp Hieronymi

doi:10.1016/j.apal.2019.05.001

When is scalar multiplication decidable?

Philipp Hieronymi

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let K be a subfield of R. The theory of R viewed as an ordered K-vector space and expanded by a predicate for Z is decidable if and only if K is a real quadratic field.

Original language	English (US)
Pages (from-to)	1162-1175
Number of pages	14
Journal	Annals of Pure and Applied Logic
Volume	170
Issue number	10
DOIs	https://doi.org/10.1016/j.apal.2019.05.001
State	Published - Oct 2019

Keywords

Decidability
Definability
Expansions of the real ordered additive group
Scalar multiplication

ASJC Scopus subject areas

Logic

Online availability

10.1016/j.apal.2019.05.001

Library availability

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Cite this

@article{e9321709d1534d748acb3bae2aac2cda,

title = "When is scalar multiplication decidable?",

abstract = "Let K be a subfield of R. The theory of R viewed as an ordered K-vector space and expanded by a predicate for Z is decidable if and only if K is a real quadratic field.",

keywords = "Decidability, Definability, Expansions of the real ordered additive group, Scalar multiplication",

author = "Philipp Hieronymi",

note = "The author was partially supported by NSF grant DMS-1300402 and by UIUC Campus Research Board award 14194.",

year = "2019",

month = oct,

doi = "10.1016/j.apal.2019.05.001",

language = "English (US)",

volume = "170",

pages = "1162--1175",

journal = "Annals of Pure and Applied Logic",

issn = "0168-0072",