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APPROXIMATING BEPPO LEVI’S PRINCIPIO DI APPROSSIMAZIONE

Published online by Cambridge University Press:  26 June 2014

RICCARDO BRUNI  and
PETER SCHUSTER
RICCARDO BRUNI
Affiliation:
DEPT. OF PHILOSOPHY, UNIVERSITY OF FLORENCE FIRENZE 50134, ITALYE-Mail:[email protected]
PETER SCHUSTER
Affiliation:
DEPT. OF PURE MATHEMATICS, UNIVERSITY OF LEEDS LEEDS LS2 9JT, UKE-Mail:[email protected]
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Abstract

We try to recast in modern terms a choice principle conceived by Beppo Levi, who called it the Approximation Principle (AP). Up to now, there was almost no discussion about Levi’s contribution, due to the quite obscure formulation of AP the author has chosen. After briefly reviewing the historical and philosophical surroundings of Levi’s proposal, we undertake our own attempt at interpreting AP. The idea underlying the principle, as well as the supposed faithfulness of our version to Levi’s original intention, are then discussed. Finally, an application of AP to a property of metric spaces is presented, with the aim of showing how AP may work in contexts where other forms of choice are commonly at use.

Keywords

Principle of approximationaxiom of choicedeductive domainscountably coverable open subsets (of a metric space)
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 20 , Issue 2 , June 2014 , pp. 141 - 169
Copyright
Copyright © The Association for Symbolic Logic 2014 

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