Forcing in proof theory

Bulletin of Symbolic Logic 10 (3):305-333 (2004)
Paul Cohen’s method of forcing, together with Saul Kripke’s related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/bsl/1102022660
 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: 22,660
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
Fernando Ferreira (1994). A Feasible Theory for Analysis. Journal of Symbolic Logic 59 (3):1001-1011.

View all 26 references / Add more references

Citations of this work BETA
Henry Towsner (2014). Ultrafilters in Reverse Mathematics. Journal of Mathematical Logic 14 (1):1450001.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

264 ( #9,995 of 1,938,821 )

Recent downloads (6 months)

23 ( #21,464 of 1,938,821 )

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.