The cofinality spectrum of the infinite symmetric group

Journal of Symbolic Logic 62 (3):902-916 (1997)
Let S be the group of all permutations of the set of natural numbers. The cofinality spectrum CF(S) of S is the set of all regular cardinals λ such that S can be expressed as the union of a chain of λ proper subgroups. This paper investigates which sets C of regular uncountable cardinals can be the cofinality spectrum of S. The following theorem is the main result of this paper. Theorem. Suppose that $V \models GCH$ . Let C be a set of regular uncountable cardinals which satisfies the following conditions. (a) C contains a maximum element. (b) If μ is an inaccessible cardinal such that $\mu = \sup(C \cap \mu)$ , then μ ∈ C. (c) If μ is a singular cardinal such that $\mu = \sup(C \cap \mu)$ , then μ + ∈ C. Then there exists a c.c.c. notion of forcing P such that $V^\mathbb{P} \models CF(S) = C$ . We shall also investigate the connections between the cofinality spectrum and pcf theory; and show that CF(S) cannot be an arbitrarily prescribed set of regular uncountable cardinals
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275578
 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
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,479
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

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

198 ( #19,131 of 1,925,766 )

Recent downloads (6 months)

1 ( #418,414 of 1,925,766 )

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.