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Axiomatics

  • Patrick Schultz
  • David I. Spivak
Chapter
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 29)

Abstract

In Chap. 4, we explained a connection between toposes, type theory, and logic. We also discussed modalities and numeric types in an arbitrary topos. In the current chapter, we will lay out the signature—meaning the atomic types, atomic terms, and axioms—for our specific topos, \(\mathcal {B}\). It turns out that our signature consists of no atomic types, one atomic term, and ten axioms.

References

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    Gierz, G., et al.: Continuous Lattices and Domains. Encyclopedia of Mathematics and Its Applications, vol. 93, pp. xxxvi+ 591. Cambridge University Press, Cambridge (2003). ISBN:0-521-80338-1. http://dx.doi.org/10.1017/CBO9780511542725
  2. [Joh02]
    Johnstone, P.T.: Sketches of an Elephant: A Topos Theory Compendium. Oxford Logic Guides, vol. 43, pp. xxii+ 468+ 71. New York: The Clarendon Press/Oxford University Press (2002). ISBN:0-19-853425-6Google Scholar
  3. [LS88]
    Lambek, J., Scott, P.J.: Introduction to Higher Order Categorical Logic. Cambridge Studies in Advanced Mathematics, vol. 7, pp. x+ 293. Reprint of the 1986 original. Cambridge University Press, Cambridge (1988). ISBN:0-521-35653-9Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Patrick Schultz
    • 1
  • David I. Spivak
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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