David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 63 (1):185-221 (1998)
Starting with D. Scott's work on the mathematical foundations of programming language semantics, interest in topology has grown up in theoretical computer science, under the slogan `open sets are semidecidable properties'. But whereas on effectively given Scott domains all such properties are also open, this is no longer true in general. In this paper a characterization of effectively given topological spaces is presented that says which semidecidable sets are open. This result has important consequences. Not only follows the classical Rice-Shapiro Theorem and its generalization to effectively given Scott domains, but also a recursion theoretic characterization of the canonical topology of effectively given metric spaces. Moreover, it implies some well known theorems on the effective continuity of effective operators such as P. Young and the author's general result which in its turn entails the theorems by Myhill-Shepherdson, Kreisel-Lacombe-Shoenfield and Ceĭtin-Moschovakis, and a result by Eršov and Berger which says that the hereditarily effective operations coincide with the hereditarily effective total continuous functionals on the natural numbers
|Keywords||No keywords specified (fix it)|
|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
Iraj Kalantari & Larry Welch (2008). On Turing Degrees of Points in Computable Topology. Mathematical Logic Quarterly 54 (5):470-482.
Similar books and articles
Jörg Flum & Juan Carlos Martinez (1988). On Topological Spaces Equivalent to Ordinals. Journal of Symbolic Logic 53 (3):785-795.
Steffen Lewitzka (2007). Abstract Logics, Logic Maps, and Logic Homomorphisms. Logica Universalis 1 (2):243-276.
Paul Bankston (1984). Expressive Power in First Order Topology. Journal of Symbolic Logic 49 (2):478-487.
Dieter Spreen (2000). Corrigendum: On Effective Topological Spaces. Journal of Symbolic Logic 65 (4):1917-1918.
Iraj Kalantari & Allen Retzlaff (1979). Recursive Constructions in Topological Spaces. Journal of Symbolic Logic 44 (4):609-625.
Viggo Stoltenberg-Hansen & John V. Tucker (2003). Computable and Continuous Partial Homomorphisms on Metric Partial Algebras. Bulletin of Symbolic Logic 9 (3):299-334.
Philip Kremer (2009). Dynamic Topological S5. Annals of Pure and Applied Logic 160 (1):96-116.
Dieter Spreen (2001). Can Partial Indexings Be Totalized? Journal of Symbolic Logic 66 (3):1157-1185.
Andrzej W. Jankowski (1986). Some Modifications of Scott's Theorem on Injective Spaces. Studia Logica 45 (2):155 - 166.
Added to index2009-01-28
Total downloads157 ( #16,787 of 1,780,746 )
Recent downloads (6 months)118 ( #5,434 of 1,780,746 )
How can I increase my downloads?