Dependent Choices and Weak Compactness

Notre Dame Journal of Formal Logic 40 (4):568-573 (1999)
  Copy   BIBTEX

Abstract

We work in set theory without the Axiom of Choice ZF. We prove that the Principle of Dependent Choices (DC) implies that the closed unit ball of a uniformly convex Banach space is weakly compact and, in particular, that the closed unit ball of a Hilbert space is weakly compact. These statements are not provable in ZF and the latter statement does not imply DC. Furthermore, DC does not imply that the closed unit ball of a reflexive space is weakly compact

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,323

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Compactness and independence in non first order frameworks.Itay Ben-Yaacov - 2005 - Bulletin of Symbolic Logic 11 (1):28-50.
Proofs of the Compactness Theorem.Alexander Paseau - 2010 - History and Philosophy of Logic 31 (1):73-98.
Freedom and weakness of will.Paul Hoffman - 2008 - Ratio 21 (1):42–54.
Measurability and degrees of strong compactness.Arthur W. Apter - 1981 - Journal of Symbolic Logic 46 (2):249-254.
A proofless proof of the Barwise compactness theorem.Mark Howard - 1988 - Journal of Symbolic Logic 53 (2):597-602.
On Finding Compactness in Aristotle.Michael Scanlan - 1983 - History and Philosophy of Logic 4 (1&2):1-8.
Level Compactness.Gillman Payette & Blaine D'Entremont - 2006 - Notre Dame Journal of Formal Logic 47 (4):545-555.

Analytics

Added to PP
2010-08-24

Downloads
26 (#614,689)

6 months
8 (#370,917)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Definability of measures and ultrafilters.David Pincus & Robert M. Solovay - 1977 - Journal of Symbolic Logic 42 (2):179-190.

Add more references