David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 47 (4):479-485 (2006)
We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing complete. We obtain the reverse mathematics result that the principle "every countable poset has a maximal filter" is equivalent to ACA₀ over RCA₀. An unbounded filter is a filter which achieves each of its lower bounds in the poset. We show that every computable poset has a \Sigma^0_1 unbounded filter, and there is a computable poset with no \Pi^0_1 unbounded filter. We show that there is a computable poset on which every unbounded filter is Turing complete, and the principle "every countable poset has an unbounded filter" is equivalent to ACA₀ over RCA₀. We obtain additional reverse mathematics results related to extending arbitrary filters to unbounded filters and forming the upward closures of subsets of computable posets
|Keywords||computable poset filter reverse mathematics|
|Categories||categorize this paper)|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Ramon Jansana (2003). Leibniz Filters Revisited. Studia Logica 75 (3):305 - 317.
Carl Jockusch Jr, Bart Kastermans, Steffen Lempp, Manuel Lerman & Reed Solomon (2009). Stability and Posets. Journal of Symbolic Logic 74 (2):693 - 711.
Andreas Blass (1990). Infinitary Combinatorics and Modal Logic. Journal of Symbolic Logic 55 (2):761-778.
Otmar Spinas (1999). Countable Filters on Ω. Journal of Symbolic Logic 64 (2):469-478.
Steffen Lempp, Charles McCoy, Russell Miller & Reed Solomon (2005). Computable Categoricity of Trees of Finite Height. Journal of Symbolic Logic 70 (1):151-215.
Jeremy Avigad (2012). Uncomputably Noisy Ergodic Limits. Notre Dame Journal of Formal Logic 53 (3):347-350.
Russell Miller (2005). The Computable Dimension of Trees of Infinite Height. Journal of Symbolic Logic 70 (1):111-141.
Michael Moses (2010). The Block Relation in Computable Linear Orders. Notre Dame Journal of Formal Logic 52 (3):289-305.
Janusz Pawlikowski (2001). Cohen Reals From Small Forcings. Journal of Symbolic Logic 66 (1):318-324.
Rod Downey, Steffen Lempp & Guohua Wu (2010). On the Complexity of the Successivity Relation in Computable Linear Orderings. Journal of Mathematical Logic 10 (01n02):83-99.
Uri Avraham & Saharon Shelah (1982). Forcing with Stable Posets. Journal of Symbolic Logic 47 (1):37-42.
Sato Kentaro (2008). Proper Semantics for Substructural Logics, From a Stalker Theoretic Point of View. Studia Logica 88 (2):295 - 324.
Anatolij Dvurečenskij & Hee Sik Kim (1998). Connections Between BCK-Algebras and Difference Posetse. Studia Logica 60 (3):421-439.
Added to index2010-08-24
Total downloads7 ( #400,000 of 1,789,795 )
Recent downloads (6 months)4 ( #195,809 of 1,789,795 )
How can I increase my downloads?