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)|
|Through your library||Configure|
Similar books and articles
Steffen Lempp & Carl Mummert (2006). Filters on Computable Posets. Notre Dame Journal of Formal Logic 47 (4):479-485.
Janusz Pawlikowski (2001). Cohen Reals From Small Forcings. Journal of Symbolic Logic 66 (1):318-324.
Uri Avraham & Saharon Shelah (1982). Forcing with Stable Posets. Journal of Symbolic Logic 47 (1):37-42.
Anatolij Dvurečenskij & Hee Sik Kim (1998). Connections Between BCK-Algebras and Difference Posetse. Studia Logica 60 (3):421-439.
Maria Luisa Dalla Chiara & Roberto Giuntini (1995). The Logics of Orthoalgebras. Studia Logica 55 (1):3 - 22.
Steffen Lempp & Manuel Lerman (1995). A General Framework for Priority Arguments. Bulletin of Symbolic Logic 1 (2):189-201.
S. O. Hansson & G. Helgesson (2003). What is Stability? Synthese 136 (2):219 - 235.
Dror Ben-Arié & Haim Judah (1993). ▵1 3-Stability. Journal of Symbolic Logic 58 (3):941 - 954.
Peter Csermely (2009). Weak Links: The Universal Key to the Stability of Networks and Complex Systems. Springer.
E. D. McCoy & Kristin Shrader-Frechette (1992). Community Ecology, Scale, and the Instability of the Stability Concept. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:184 - 199.
Lydia Mechtenberg (2004). The Stability Theory of Knowledge and Belief Revision: Comments on Rott. Erkenntnis 61 (2-3):495 - 507.
Rod Downey, Denis R. Hirschfeldt, Steffen Lempp & Reed Solomon (2001). A Δ02 Set with No Infinite Low Subset in Either It or its Complement. Journal of Symbolic Logic 66 (3):1371 - 1381.
John Lemons (1981). Cooperation and Stability as a Basis for Environmental Ethics. Environmental Ethics 3 (3):219-230.
Sorry, there are not enough data points to plot this chart.
Added to index2010-09-12
Recent downloads (6 months)0
How can I increase my downloads?