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The papers on abstract Stone duality may be obtained from

[O]
 Paul Taylor, Foundations for Computable Topology.
in Giovanni Sommaruga (ed.),
Foundational Theories of Mathematics, Kluwer 2011.
 [A]
 Paul Taylor, Sober spaces and continuations.
Theory and Applications of Categories, 10(12):248–299, 2002.
 [B]
 Paul Taylor, Subspaces in abstract Stone duality.
Theory and Applications of Categories, 10(13):300–366, 2002.
 [C]
 Paul Taylor, Geometric and higher order logic using abstract Stone duality.
Theory and Applications of Categories, 7(15):284–338, 2000.
 [D]
 Paul Taylor, NonArtin gluing in recursion theory and lifting in abstract
Stone duality.
2000.
 [E]
 Paul Taylor, Inside every model of Abstract Stone Duality lies an Arithmetic Universe.
Electronic Notes in Theoretical Computer Science 122
(2005) 247296.
 [F]
 Paul Taylor, Scott domains in abstract Stone duality.
March 2002.
 [G–]
 Paul Taylor, Local compactness and the Baire category theorem in abstract
Stone duality.
Electronic Notes in Theoretical Computer Science 69,
Elsevier, 2003.
 [G]
 Paul Taylor, Computably based locally compact spaces.
Logical Methods in Computer Science, 2 (2006) 1–70.
 [H–]
 Paul Taylor, An elementary theory of the category of locally compact locales.
APPSEM Workshop, Nottingham, March 2003.
 [H]
 Paul Taylor, An elementary theory of various categories of spaces and locales.
November 2004.
 [I]
 Andrej Bauer and Paul Taylor, The Dedekind reals in abstract Stone duality.
Mathematical Structures in Computer Science,
19 (2009) 757–838.
 [J]
 Paul Taylor, A λcalculus for real analysis.
Journal of Logic and Analysis, 2(5), 1–115 (2010)
 [K]
 Paul Taylor, Interval analysis without intervals.
February 2006.
 [L]
 Paul Taylor, Tychonov’s theorem in abstract Stone duality.
September 2004.
 [N]
 Paul Taylor, Computability in locally compact spaces.
2010.
 [AA]
 Paul Taylor, Equideductive categories and their logic.
2010.
 [BB]
 Paul Taylor, An existential quantifier for topology.
2010.
 [CC]
 Paul Taylor, Cartesian closed categories with subspaces.
2009.
 [DD]
 Paul Taylor, The Phoa principle in equideductive topology.
2010.
 [EE]
 Paul Taylor, Discrete mathematics in equideductive topology.
2010.
 [FF]
 Paul Taylor, Equideductive topology.
2010.
 [GG]
 Paul Taylor, Underlying sets in equideductive topology.
2010.