REFERENCES[BF] S., Baratella and R., Ferro, A theory of sets with the negation of the axiom of infinity, Mathematical Logic Quarterly, vol. 39 (1993), no. 3, pp. 338–352.
[Ba] J., Barwise, Admissible Sets and Structures, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1975.
[Be-1] P., Bernays, A system of axiomatic set theory. Part II, The Journal of Symbolic Logic, vol. 6 (1941), pp. 1–17.
[Be-2] P., Bernays, A system of axiomatic set theory. Part VII, The Journal of Symbolic Logic, vol. 19 (1954), pp. 81–96.
[CK] C. C., Chang and H. J., Keisler, Model Theory, North-Holland, Amsterdam, 1973.
[Fr] R., Frucht, Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Mathematica, vol. 6 (1939), pp. 239–250.
[HP] P., Hájek and P., Pudlák, Metamathematics of First-Order Arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1998.
[HV] P., Hájek and P., Vopěnka, Über die Gültigkeit des Fundierungsaxioms in speziellen Systemen der Mengentheorie, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 9 (1963), pp. 235–241.
[Ha] K., Hauschild, Bemerkungen, das Fundierungsaxiom betreffend, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 12 (1966), pp. 51–56.
[Ho] W., Hodges, Model Theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993.
[IT] K, Ikeda and A., Tsuboi, Nonstandard models that are definable in models of Peano arithmetic, Mathematical Logic Quarterly, vol. 53 (2007), no. 1, pp. 27–37.
[Ka] R., Kaye, Tennenbaum's theorem for models of arithmetic, this volume.
[KW] R., Kaye and T., Wong, On interpretations of arithmetic and set theory, Notre Dame Journal of Formal Logic, vol. 48 (2007), no. 4, pp. 497–510.
[KS] R., Kossak and J. H., Schmerl, The Structure of Models of Peano Arithmetic, Oxford Logic Guides, vol. 50, The Clarendon Press Oxford University Press, Oxford, 2006, Oxford Science Publications.
[Kr] G., Kreisel, Note on arithmetic models for consistent formulae of the predicate calculus. II, Actes du XIème Congrès International de Philosophie, Bruxelles, 20–26 Août 1953, vol. XIV, North-Holland, Amsterdam, 1953, pp. 39–49.
[Li] P., Lindström, Aspects of Incompleteness, second ed., Lecture Notes in Logic, vol. 10, Association for Symbolic Logic, Urbana, IL, 2003.
[Lo] L., Lovász, Combinatorial Problems and Exercises, AMS Chelsea Publishing, Providence, RI, 2007, Corrected reprint of the 1993 second edition.
[Mac] S. Mac, Lane, Categories for the Working Mathematician, second ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998.
[MZ] A., Mancini and D., Zambella, A note on recursive models of set theories, Notre Dame Journal of Formal Logic, vol. 42 (2001), no. 2, pp. 109–115.
[Moh] S., Mohsenipour, A recursive nonstandard model for open induction with GCD property and cofinal primes, Logic in Tehran, Lecture Notes in Logic, vol. 26, ASL, La Jolla, CA, 2006, pp. 227–238.
[Mos] A., Mostowski, On a system of axioms which has no recursively enumerable arithmetic model, Fundamenta Mathematicae, vol. 40 (1953), pp. 56–61.
[NP] J., Nešetřil and A., Pultr, A note on homomorphism-independent families, Combinatorics (Prague, 1998), Discrete Mathematics, vol. 235 (2001), no. 1-3, pp. 327–334.
[P] E. A., Perminov, The number of rigid graphs that are mutually nonimbeddable into one another, Izvestiya Vysshikh Uchebnykh Zavedeniî. Matematika, (1985), no. 8, pp. 77–78, 86.
[Ra] M., Rabin, On recursively enumerable and arithmetic models of set theory, The Journal of Symbolic Logic, vol. 23 (1958), pp. 408–416.
[Ri] L., Rieger, A contribution to Gödel's axiomatic set theory, Czechoslovak Mathematical Journal, vol. 7 (1957), pp. 323–357.
[Sch-1] J. H., Schmerl, An axiomatization for a class of two-cardinal models, The Journal of Symbolic Logic, vol. 42 (1977), no. 2, pp. 174–178.
[Sch-2] J. H., Schmerl, Tennenbaum's theorem and recursive reducts, this volume.
[Sco] D., Scott, On a theorem of Rabin, Nederl. Akad. Wetensch. Proc. Ser. A 63 = Indag. Math., vol. 22 (1960), pp. 481–484.
[Vi-1] A., Visser, Faith & Falsity, Annals of Pure and Applied Logic, vol. 131 (2005), no. 1-3, pp. 103–131.
[Vi-2] A., Visser, Categories of theories and interpretations, Logic in Tehran, Lecture Notes in Logic, vol. 26, ASL, La Jolla, CA, 2006, pp. 284–341.
[Vo-1] P., Vopěnka, Axiome der Theorie endlicher Mengen, Československá Akademie Věd. Časopis Pro Pěstování Matematiky, vol. 89 (1964), pp. 312–317.
[Vo-2] P., Vopěnka, Mathematics in the Alternative Set Theory, Teubner-Verlag, Leipzig, 1979.