Developing arithmetic in set theory without infinity: some historical remarks

History and Philosophy of Logic 8 (2):201-213 (1987)
In this paper some of the history of the development of arithmetic in set theory is traced, particularly with reference to the problem of avoiding the assumption of an infinite set. Although the standard method of singling out a sequence of sets to be the natural numbers goes back to Zermelo, its development was more tortuous than is generally believed. We consider the development in the light of three desiderata for a solution and argue that they can probably not all be satisfied simultaneously
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1080/01445348708837116
 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: 24,453
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
Kurt Gödel (1986). Collected Works. Oxford University Press.

View all 20 references / Add more references

Citations of this work BETA
Akihiro Kanamori (2004). Zermelo and Set Theory. Bulletin of Symbolic Logic 10 (4):487-553.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

35 ( #137,420 of 1,925,264 )

Recent downloads (6 months)

1 ( #418,201 of 1,925,264 )

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.