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A FUNDAMENTAL DICHOTOMY FOR DEFINABLY COMPLETE EXPANSIONS OF ORDERED FIELDS

Published online by Cambridge University Press:  22 December 2015

ANTONGIULIO FORNASIERO  and
PHILIPP HIERONYMI
ANTONGIULIO FORNASIERO
Affiliation:
SECONDA UNIVERSITÀ DI NAPOLI VIALE LINCOLN 5 81100 CASERTAITALYE-mail:antongiulio.fornasiero@gmail.comURL: http://www.dm.unipi.it/∼fornasiero
PHILIPP HIERONYMI
Affiliation:
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN DEPARTMENT OF MATHEMATICS 1409 W. GREEN STREET URBANA, IL 61801, USAE-mail: phierony@illinois.edu
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Abstract

An expansion of a definably complete field either defines a discrete subring, or the image of every definable discrete set under every definable map is nowhere dense. As an application we show a definable version of Lebesgue’s differentiation theorem.

Keywords

03C64Definably completesecond-order arithmeticLebesgue’s differentiation theorem
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 4 , December 2015 , pp. 1091 - 1115
Copyright
Copyright © The Association for Symbolic Logic 2015 

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