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.
A fundamental dichotomy for definably complete expansions of ordered fields / Fornasiero, Antongiulio; Hieronymi, Philipp. - In: THE JOURNAL OF SYMBOLIC LOGIC. - ISSN 0022-4812. - STAMPA. - 80:(2015), pp. 1091-1115. [10.1017/jsl.2014.10]
A fundamental dichotomy for definably complete expansions of ordered fields
Fornasiero, Antongiulio;
2015
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.
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