A geometric form of the axiom of choice

Consider the following well-known result from the theory of normed linear spaces ([2], p. 80, 4(b)): (g) the unit ball of the (continuous) dual of a normed linear space over the reals has an extreme point. The standard proof of (~) uses the axiom of choice (AG); thus the implication AC~(w) can be proved in set theory. In this paper we show that this implication can be reversed, so that (*) is actually eq7I2valent to the axiom of choice. From this we derive various corollaries, for example: the conjunction of the Boolean prime ideal theorem and the Krein-Milman theorem implies the axiom of choice, and the Krein-Milman theorem is not derivable from the Boolean prime ideal theorem.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index Translate to english
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,707
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles
John Bell (2003). Some New Intuitionistic Equivalents of Zorn's Lemma. Archive for Mathematical Logic 42 (8):811-814.
Mitchell Spector (1988). Ultrapowers Without the Axiom of Choice. Journal of Symbolic Logic 53 (4):1208-1219.
Harvey Friedman (2000). Does Mathematics Need New Axioms? Bulletin of Symbolic Logic 6 (4):401 - 446.
John L. Bell, The Axiom of Choice. Stanford Encyclopedia of Philosophy.

Monthly downloads

Added to index


Total downloads

10 ( #235,035 of 1,726,249 )

Recent downloads (6 months)

1 ( #369,877 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.