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Doing Without Turing Machines: Constructivism and Formal Topology

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Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

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Abstract

We add some new insights, and thus hopefully contribute to give new impetus, to an old theme: constructive mathematics, and topology in particular, can be thought of as an abstract way to deal with computation.

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References

  1. Bishop, E.: Foundations of constructive analysis. McGraw-Hill Book Co, New York (1967)

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  2. Maietti, M.E.: Quotients over minimal type theory (this volume)

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  3. Maietti, M.E., Sambin, G.: Toward a miminalist foundation for constructive mathematics, in From Sets and Types to Topology and Analysis. In: Crosilla, L., Schuster, P. (eds.) Towards practicable foundations for constructive mathematics, Oxford Logic Guides, pp. 91–114. Clarendon Press, Oxford (2005)

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  4. Martin-Löf, P.: Notes on Constructive Mathematics, Almqvist & Wiksell (1970)

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  5. Sambin, G.: Intuitionistic formal spaces – a first communication. In: Skordev, D. (ed.) Mathematical Logic and its Applications, Plenum, pp. 187–204 (1987)

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© 2007 Springer-Verlag Berlin Heidelberg

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Sambin, G. (2007). Doing Without Turing Machines: Constructivism and Formal Topology. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_71

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  • DOI: https://doi.org/10.1007/978-3-540-73001-9_71

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

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