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Henk Barendregt. The Lambda Calculus: its Syntax and Semantics. Number 103 in Studies in Logic and the Foundations of Mathematics. North-Holland, 1981. Second edition, 1984.
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The papers on abstract Stone duality may be obtained from

www.Paul Taylor.EU/ASD
Paul Taylor, Foundations for Computable Topology. in Giovanni Sommaruga (ed.), Foundational Theories of Mathematics, Kluwer 2011.
Paul Taylor, Sober spaces and continuations. Theory and Applications of Categories, 10(12):248–299, 2002.
Paul Taylor, Subspaces in abstract Stone duality. Theory and Applications of Categories, 10(13):300–366, 2002.
Paul Taylor, Geometric and higher order logic using abstract Stone duality. Theory and Applications of Categories, 7(15):284–338, 2000.
Paul Taylor, Non-Artin gluing in recursion theory and lifting in abstract Stone duality. 2000.
Paul Taylor, Inside every model of Abstract Stone Duality lies an Arithmetic Universe. Electronic Notes in Theoretical Computer Science 122 (2005) 247-296.
Paul Taylor, Scott domains in abstract Stone duality. March 2002.
Paul Taylor, Local compactness and the Baire category theorem in abstract Stone duality. Electronic Notes in Theoretical Computer Science 69, Elsevier, 2003.
Paul Taylor, Computably based locally compact spaces. Logical Methods in Computer Science, 2 (2006) 1–70.
Paul Taylor, An elementary theory of the category of locally compact locales. APPSEM Workshop, Nottingham, March 2003.
Paul Taylor, An elementary theory of various categories of spaces and locales. November 2004.
Andrej Bauer and Paul Taylor, The Dedekind reals in abstract Stone duality. Mathematical Structures in Computer Science, 19 (2009) 757–838.
Paul Taylor, A λ-calculus for real analysis. Journal of Logic and Analysis, 2(5), 1–115 (2010)
Paul Taylor, Interval analysis without intervals. February 2006.
Paul Taylor, Tychonov’s theorem in abstract Stone duality. September 2004.
Paul Taylor, Computability in locally compact spaces. 2010.
Paul Taylor, Equideductive categories and their logic. 2010.
Paul Taylor, An existential quantifier for topology. 2010.
Paul Taylor, Cartesian closed categories with subspaces. 2009.
Paul Taylor, The Phoa principle in equideductive topology. 2010.
Paul Taylor, Discrete mathematics in equideductive topology. 2010.
Paul Taylor, Equideductive topology. 2010.
Paul Taylor, Underlying sets in equideductive topology. 2010.

Previous Up Next Acknowledgements Previous Up


This paper evolved from [G–], which included roughly Sections 58 and 11 of the present version. It was presented at Category Theory and Computer Science 9, in Ottawa on 17 August 2002, and at Domains Workshop 6 in Birmingham a month later. The characterisation of locally compact objects using effective bases (Section 6) had been announced on categories on 30 January 2002.

The earlier version also showed that any object has a filter basis, and went on to prove Baire’s category theorem, that the intersection of any sequence of dense open subobjects (of any locally compact overt object) is dense. These arguments were adapted from the corresponding ones in the theory of continuous lattices [GHK++80, Sections I 3.3 and 3.43].

I would like to thank Andrej Bauer, Martƒn Escardó, Peter Johnstone, Achim Jung, Jimmie Lawson, Graham White and the CTCS and LMCS referees for their comments. Graham White has given continuing encouragement throughout the abstract Stone duality project, besides being an inexhaustible source of mathematical ideas.

This research is now supported by UK EPSRC project GR/S58522, but this funding was obtained in part on the basis of the work in this paper. Apart from 5.19, 12.13, 12.14, 15.3, 15.5, 16.15 and 17.6, the work here was carried out during a period of unemployment, supported entirely from my own savings. However, I would have been unable to do this without the companionship and emotional support of my partner, Richard Symes.

© 2002–5 Paul Taylor.

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