Journal of Symbolic Logic 74 (2):693 - 711 (2009)

Abstract
Hirschfeldt and Shore have introduced a notion of stability for infinite posets. We define an arguably more natural notion called weak stability, and we study the existence of infinite computable or low chains or antichains, and of infinite $\Pi _1^0 $ chains and antichains, in infinite computable stable and weakly stable posets. For example, we extend a result of Hirschfeldt and Shore to show that every infinite computable weakly stable poset contains either an infinite low chain or an infinite computable antichain. Our hardest result is that there is an infinite computable weakly stable poset with no infinite $\Pi _1^0 $ chains or antichains. On the other hand, it is easily seen that every infinite computable stable poset contains an infinite computable chain or an infinite $\Pi _1^0 $ antichain. In Reverse Mathematics, we show that SCAC, the principle that every infinite stable poset contains an infinite chain or antichain, is equivalent over RCA₀ to WSCAC, the corresponding principle for weakly stable posets
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1243948336
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 72,577
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

Filters on Computable Posets.Steffen Lempp & Carl Mummert - 2006 - Notre Dame Journal of Formal Logic 47 (4):479-485.
Cohen Reals From Small Forcings.Janusz Pawlikowski - 2001 - Journal of Symbolic Logic 66 (1):318-324.
Forcing with Stable Posets.Uri Avraham & Saharon Shelah - 1982 - Journal of Symbolic Logic 47 (1):37-42.
A General Framework for Priority Arguments.Steffen Lempp & Manuel Lerman - 1995 - Bulletin of Symbolic Logic 1 (2):189-201.
What is Stability?S. Hansson & G. Helgesson - 2003 - Synthese 136 (2):219 - 235.
▵1 3-Stability.Dror Ben-Arié & Haim Judah - 1993 - Journal of Symbolic Logic 58 (3):941 - 954.
Community Ecology, Scale, and the Instability of the Stability Concept.E. D. McCoy & Kristin Shrader-Frechette - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:184 - 199.

Analytics

Added to PP index
2010-09-12

Total views
264 ( #42,590 of 2,533,585 )

Recent downloads (6 months)
1 ( #390,861 of 2,533,585 )

How can I increase my downloads?

Downloads

My notes