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HAMEL SPACES AND DISTAL EXPANSIONS

Published online by Cambridge University Press:  29 August 2019

ALLEN GEHRET  and
TRAVIS NELL
ALLEN GEHRET
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA LOS ANGELES, LOS ANGELES, CA90095, USA E-mail: allen@math.ucla.edu
TRAVIS NELL
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN URBANA, IL61801, USA E-mail: tnell2@illinois.edu
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Abstract

In this note, we construct a distal expansion for the structure $$\left( {; + , < ,H} \right)$$, where $H \subseteq $ is a dense $Q$-vector space basis of $R$ (a so-called Hamel basis). Our construction is also an expansion of the dense pair $\left( {; + , < ,} \right)$ and has full quantifier elimination in a natural language.

Keywords

Primary 03C64Secondary 03C4506F20distalitydp-rankindependence propertyo-minimalitydense pairsHamel basis
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 1 , March 2020 , pp. 422 - 438
Copyright
Copyright © The Association for Symbolic Logic 2019 

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