@book(Adamek,
 author       = {J.~Ad\'{a}mek and J~Rosick\'{y}},
 year         = {1994},
 title        = {Locally presentable and accessible categories},
 publisher    = {Cambridge University Press},
 doi          = {10.1017/CBO9780511600579},
)
@book(Bell,
 author       = {J.~L. Bell},
 year         = {1988},
 title        = {Toposes and Local Set Theories},
 series       = {Oxford Logic Guides},
 volume       = {14},
 publisher    = {Oxford Univ. Press},
)
@article(Orbits,
 author       = {J.~B\'{e}nabou and B.~Loiseau},
 year         = {1994},
 title        = {Orbits and monoids in a topos},
 journal      = {J. of Pure and Applied Algebra},
 volume       = {92},
 number       = {1},
 doi          = {10.1016/0022-4049(94)90045-0},
 url          = {http://www.sciencedirect.com/science/article/pii/0022404994900450},
)
@incollection(Copeland,
 author       = {B.~Jack Copeland},
 year         = {2015},
 title        = {The Church-Turing Thesis},
 editor       = {Edward~N. Zalta},
 booktitle    = {The Stanford Encyclopedia of Philosophy},
 edition      = {summer 2015},
)
@article(Dershowitz:08,
 author       = {Nachum Dershowitz and Yuri Gurevich},
 year         = {2008},
 title        = {A natural axiomatization of computability and proof of {C}hurch's Thesis},
 journal      = {Bulletin of Symbolic Logic},
 volume       = {14},
 number       = {03},
 pages        = {299--350},
 doi          = {10.2178/bsl/1231081370},
)
@book(Eilenberg:70,
 author       = {S.~Eilenberg and C.C. Elgot},
 year         = {1970},
 title        = {Recursiveness},
 series       = {ACM monograph series},
 publisher    = {Academic Press},
 url          = {https://books.google.com.br/books?id=hvruAAAAMAAJ},
)
@book(lfp-cats,
 author       = {P.~Gabriel and F.~Ulmer},
 year         = {1971},
 title        = {Lokal pr\"{a}sentierbare Kategorien},
 series       = {Lecture Notes in Mathematics},
 volume       = {221},
 publisher    = {Springer-Verlag},
)
@book(Goldblatt,
 author       = {Robert. Goldblatt},
 year         = {1979},
 title        = {Topoi, the categorial analysis of logic},
 publisher    = {North-Holland},
)
@article(infinite,
 author       = {Joel~David Hamkins and Andy Lewis},
 year         = {2000},
 title        = {Infinite time {T}uring machines},
 journal      = {J. Symbolic Logic},
 volume       = {65},
 number       = {2},
 pages        = {567--604},
 doi          = {10.2307/2586556},
)
@book(Hopcroft,
 author       = {J.E. Hopcroft and R.~Motwani and J.D. Ullman},
 year         = {2001},
 title        = {Introduction to Automata Theory, Languages, and Computation},
 series       = {Addison-Wesley series in computer science},
 publisher    = {Addison-Wesley},
 url          = {https://books.google.com.br/books?id=omIPAQAAMAAJ},
)
@incollection(Hyland,
 author       = {J.M.E. Hyland},
 year         = {1982},
 title        = {The Effective Topos},
 editor       = {A.S. Troelstra and D.~van Dalen},
 booktitle    = {The L. E. J. Brouwer Centenary SymposiumProceedings of the Conference held in Noordwijkerhout},
 series       = {Studies in Logic and the Foundations of Mathematics},
 volume       = {110},
 publisher    = {Elsevier},
 pages        = {165 -- 216},
 doi          = {10.1016/S0049-237X(09)70129-6},
 url          = {http://www.sciencedirect.com/science/article/pii/S0049237X09701296},
)
@article(Johnstone:AlgUniv,
 author       = {{P}eter {J}ohnstone},
 year         = {1979},
 title        = {{A}utomorphisms of $\Omega$},
 journal      = {{A}lgebra {U}niversalis},
 volume       = {9},
 number       = {1},
)
@book(Johnstone,
 author       = {P.~T. Johnstone},
 year         = {1977},
 title        = {Topos Theory},
 publisher    = {Academic Press},
)
@incollection(Kock1975,
 author       = {A.~Kock and P.~Lecouturier and C.~J. Mikkelsen},
 year         = {1975},
 title        = {Model Theory and Topoi: A Collection of Lectures by Various Authors},
 chapter      = {Some topos theoretic concepts of finiteness},
 publisher    = {Springer Berlin Heidelberg},
 address      = {Berlin, Heidelberg},
 pages        = {209--283},
 doi          = {10.1007/BFb0061297},
)
@book(Machtey,
 author       = {Michael. Machtey and Paul Young},
 year         = {1978},
 title        = {An introduction to the general theory of algorithms},
 publisher    = {North-Holland},
)
@book(Mclarty,
 author       = {Colin McLarty},
 year         = {1992},
 title        = {Elementary categories, elementary toposes},
 publisher    = {Oxford University Press},
)
@book(Rogers,
 author       = {H.~Rogers},
 year         = {1987},
 title        = {{T}heory of {R}ecursive {F}unctions and {E}ffective {C}omputability},
 publisher    = {{MIT} {P}ress},
)
@article(Shapiro:11,
 author       = {Stewart Shapiro},
 year         = {2011},
 title        = {Varieties of pluralism and relativism for logic},
 journal      = {A companion to relativism},
 pages        = {526--552},
 doi          = {10.1002/9781444392494.ch27},
)
@incollection(Sieg,
 author       = {Wilfried Sieg},
 year         = {2008},
 title        = {Church Without Dogma: Axioms for Computability},
 editor       = {S.Barry Cooper and Benedikt Löwe and Andrea Sorbi},
 booktitle    = {New Computational Paradigms},
 publisher    = {Springer New York},
 pages        = {139--152},
 doi          = {10.1007/978-0-387-68546-5\_7},
)
@misc(Squire1997,
 author       = {R.~Squire},
 howpublished = {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},
)
@article(TarskiFinite,
 author       = {Alfred Tarski},
 year         = {1924},
 title        = {Sur les ensembles finis},
 journal      = {Fundamenta Mathematicae},
 volume       = {6},
 pages        = {45--95},
)