An Incompleteness Theorem for [image]

Journal of Symbolic Logic 69 (2):612 - 616 (2004)
Let n be a positive integer. By a $\beta_{n}-model$ we mean an $\omega-model$ which is elementary with respect to $\sigma_{n}^{1}$ formulas. We prove the following $\beta_{n}-model$ version of $G\ddot{o}del's$ Second Incompleteness Theorem. For any recursively axiomatized theory S in the language of second order arithmetic, if there exists a $\beta_{n}-model$ of S, then there exists a $\beta_{n}-model$ of S + "there is no countable $\beta_{n}-model$ of S". We also prove a $\beta_{n}-model$ version of $L\ddot{o}b's$ Theorem. As a corollary, we obtain a $\beta_{n}-model$ which is not a $\beta_{n+1}-model$
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
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 23,217
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

No citations found.

Add more citations

Similar books and articles
Ali Enayat (2001). Power-Like Models of Set Theory. Journal of Symbolic Logic 66 (4):1766-1782.
Ali Enayat (2004). Leibnizian Models of Set Theory. Journal of Symbolic Logic 69 (3):775-789.

Monthly downloads

Added to index


Total downloads

25 ( #189,821 of 1,939,385 )

Recent downloads (6 months)

17 ( #40,335 of 1,939,385 )

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.