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143Logicism, intuitionism, and formalism - What has become of them? (edited book)Springer. 2008.The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were als…Read more
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39Computable and continuous partial homomorphisms on metric partial algebrasBulletin of Symbolic Logic 9 (3): 299-334. 2003.We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topol…Read more
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26On computational complexity in weakly admissible structuresJournal of Symbolic Logic 45 (2): 353-358. 1980.
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23A logical presentation of the continuous functionalsJournal of Symbolic Logic 62 (3): 1021-1034. 1997.
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20Domain interpretations of martin-löf’s partial type theoryAnnals of Pure and Applied Logic 48 (2): 135-196. 1990.
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202003 european summer meeting of the association for symbolic logic logic colloquim '03, helsinki, finland, August 14-20, 2003' (review)Bulletin of Symbolic Logic 10 (2): 234-280. 2004.
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20Stability of representations of effective partial algebrasMathematical Logic Quarterly 57 (2): 217-231. 2011.An algebra is effective if its operations are computable under some numbering. When are two numberings of an effective partial algebra equivalent? For example, the computable real numbers form an effective field and two effective numberings of the field of computable reals are equivalent if the limit operator is assumed to be computable in the numberings . To answer the question for effective algebras in general, we give a general method based on an algebraic analysis of approximations by elemen…Read more
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14Computable and Continuous Partial Homomorphisms on Metric Partial AlgebrasBulletin of Symbolic Logic 9 (3): 299-334. 2003.We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topol…Read more
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8He rose and jc ShepherdsonIn Edward R. Griffor (ed.), Handbook of Computability Theory, Elsevier. pp. 359. 1999.
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6Finite injury arguments in infinite computation theoriesAnnals of Mathematical Logic 16 (1): 57-80. 1979.
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4C. TRETKOFF [1988] Complexity, combinatorial group theory and the language of palutators, Theoret. Comput. Sci., 56. pp. 253-275 (review)In Edward R. Griffor (ed.), Handbook of Computability Theory, Elsevier. pp. 140--445. 1999.
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2A Logical Presentation Of The Continuous FunctionalsJournal of Symbolic Logic 62 (3): 1021-1034. 1997.