✦ LIBER ✦

Continuity properties of preference relations

✍ Scribed by Marian A. Baroni; Douglas S. Bridges

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 104 KB
Volume: 54
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200710059

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Various types of continuity for preference relations on a metric space are examined constructively. In particular, necessary and sufficient conditions are given for an order‐dense, strongly extensional preference relation on a complete metric space to be continuous. It is also shown, in the spirit of constructive reverse mathematics, that the continuity of sequentially continuous, order‐dense preference relations on complete, separable metric spaces is connected to Ishihara's principleBD‐ℕ, and therefore is not provable within Bishop‐style constructive mathematics alone. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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