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8Lifschitz realizability as a topological constructionJournal of Symbolic Logic 85 (4): 1342-1375. 2020.We develop a number of variants of Lifschitz realizability for $\mathbf {CZF}$ by building topological models internally in certain realizability models. We use this to show some interesting metamathematical results about constructive set theory with variants of the lesser limited principle of omniscience including consistency with unique Church’s thesis, consistency with some Brouwerian principles and variants of the numerical existence property.
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6On the proof-theoretic strength of monotone induction in explicit mathematicsAnnals of Pure and Applied Logic 85 (1): 1-46. 1997.
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5Investigations of Subsystems of Second Order Arithmetic and Set Theory in Strength between Π11 -CA and Δ12 -CA + BI: Part I (review)In Ralf Schindler (ed.), Ways of Proof Theory, De Gruyter. pp. 363-440. 2010.
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4Formal Baire Space in Constructive Set TheoryIn Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger (eds.), Logic, Construction, Computation, De Gruyter. pp. 123-136. 2012.
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4Explicit Mathematics with the Monotone Fixed Point Principle. II: ModelsJournal of Symbolic Logic 64 (2): 517-550. 1999.This paper continues investigations of the monotone fixed point principle in the context of Feferman's explicit mathematics begun in [14]. Explicit mathematics is a versatile formal framework for representing Bishop-style constructive mathematics and generalized recursion theory. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications possesses a least fixed point. To be m…Read more
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4Explicit Mathematics with the Monotone Fixed Point PrincipleJournal of Symbolic Logic 63 (2): 509-542. 1998.The context for this paper is Feferman's theory of explicit mathematics, a formal framework serving many purposes. It is suitable for representing Bishop-style constructive mathematics as well as generalized recursion, including direct expression of structural concepts which admit self-application. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications possesses a least f…Read more
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3Admissible extensions of subtheories of second order arithmeticAnnals of Pure and Applied Logic 175 (7): 103425. 2024.
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On Relating Theories: Proof-Theoretical ReductionIn Stefania Centrone, Sara Negri, Deniz Sarikaya & Peter M. Schuster (eds.), Mathesis Universalis, Computability and Proof, Springer Verlag. 2019.
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University of LeedsRegular Faculty
Leeds, West Yorkshire, United Kingdom of Great Britain and Northern Ireland
Areas of Interest
19th Century Philosophy |
20th Century Philosophy |