References

  1. J. Adámek & J Rosický (1994): Locally presentable and accessible categories. Cambridge University Press, doi:10.1017/CBO9780511600579.
  2. J. L. Bell (1988): Toposes and Local Set Theories. Oxford Logic Guides 14. Oxford Univ. Press.
  3. J. Bénabou & B. Loiseau (1994): Orbits and monoids in a topos. J. of Pure and Applied Algebra 92(1), doi:10.1016/0022-4049(94)90045-0. Available at http://www.sciencedirect.com/science/article/pii/0022404994900450.
  4. B. Jack Copeland (2015): The Church-Turing Thesis. In: Edward N. Zalta: The Stanford Encyclopedia of Philosophy, summer 2015 edition.
  5. Nachum Dershowitz & Yuri Gurevich (2008): A natural axiomatization of computability and proof of Church's Thesis. Bulletin of Symbolic Logic 14(03), pp. 299–350, doi:10.2178/bsl/1231081370.
  6. S. Eilenberg & C.C. Elgot (1970): Recursiveness. ACM monograph series. Academic Press. Available at https://books.google.com.br/books?id=hvruAAAAMAAJ.
  7. P. Gabriel & F. Ulmer (1971): Lokal präsentierbare Kategorien. Lecture Notes in Mathematics 221. Springer-Verlag.
  8. Robert. Goldblatt (1979): Topoi, the categorial analysis of logic. North-Holland.
  9. Joel David Hamkins & Andy Lewis (2000): Infinite time Turing machines. J. Symbolic Logic 65(2), pp. 567–604, doi:10.2307/2586556.
  10. J.E. Hopcroft, R. Motwani & J.D. Ullman (2001): Introduction to Automata Theory, Languages, and Computation. Addison-Wesley series in computer science. Addison-Wesley. Available at https://books.google.com.br/books?id=omIPAQAAMAAJ.
  11. J.M.E. Hyland (1982): The Effective Topos. In: A.S. Troelstra & D. van Dalen: The L. E. J. Brouwer Centenary SymposiumProceedings of the Conference held in Noordwijkerhout, Studies in Logic and the Foundations of Mathematics 110. Elsevier, pp. 165 – 216, doi:10.1016/S0049-237X(09)70129-6. Available at http://www.sciencedirect.com/science/article/pii/S0049237X09701296.
  12. Peter Johnstone (1979): Automorphisms of Ω. Algebra Universalis 9(1).
  13. P. T. Johnstone (1977): Topos Theory. Academic Press.
  14. A. Kock, P. Lecouturier & C. J. Mikkelsen (1975): Model Theory and Topoi: A Collection of Lectures by Various Authors, chapter Some topos theoretic concepts of finiteness. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 209–283, doi:10.1007/BFb0061297.
  15. Michael. Machtey & Paul Young (1978): An introduction to the general theory of algorithms. North-Holland.
  16. Colin McLarty (1992): Elementary categories, elementary toposes. Oxford University Press.
  17. H. Rogers (1987): Theory of Recursive Functions and Effective Computability. MIT Press.
  18. Stewart Shapiro (2011): Varieties of pluralism and relativism for logic. A companion to relativism, pp. 526–552, doi:10.1002/9781444392494.ch27.
  19. Wilfried Sieg (2008): Church Without Dogma: Axioms for Computability. In: S.Barry Cooper, Benedikt Löwe & Andrea Sorbi: New Computational Paradigms. Springer New York, pp. 139–152, doi:10.1007/978-0-387-68546-5_7.
  20. R. Squire. Appears as private communication in many references in many articles. We used as reference the Master dissertation of Peter Arndt, Universidade de Campinas, Departamento de Filosofia, 2005.
  21. Alfred Tarski (1924): Sur les ensembles finis. Fundamenta Mathematicae 6, pp. 45–95.

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