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Possible m-diagrams ofmodels of arithmetic

Published online by Cambridge University Press:  31 March 2017

Stephen G. Simpson
Affiliation:
Pennsylvania State University
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Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] Andrew, Arana, Solovay's theorem cannot be simplified, Annals of Pure and Applied Logic, vol. 112 (2001), pp. 27–41.Google Scholar
[2] Jon, Barwise (editor), Handbook of mathematical logic, Studies in Logic and the Foundations ofMathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977.
[3] Solomon, Feferman, Arithmetically definable models of formalizable arithmetic, Notices of the American Mathematical Society, vol. 5 (1958), p. 679.Google Scholar
[4] KurtGödel, Über formal unentscheidhare Sätze der PrincipiaMathematica und verwandter Systeme I,Collected works (Solomon Feferman et al., editors), vol. 1, Oxford University Press, New York and Oxford, 1986, pp. 145–195.
[5] Leo, Harrington, Building non-standard models of Peano Arithmetic, Unpublished notes, 1979.
[6] Julia F., Knight, True approximations and models of arithmetic, Models and computability (B., Cooper and J., Truss, editors), Cambridge University Press, New York, 1999, pp. 255–278.
[7] Angus, Macintyre and David, Marker, Degrees of recursively saturated models,Transactions of the American Mathematical Society, vol. 282 (1984), pp. 539–554.
[8] David, Marker, Degrees of models of true arithmetic,Proceedings of the Herbrand Symposium (J., Stern, editor), North-Holland, 1982, pp. 233–242.
[9] David, Marker, Degrees of models of arithmetic, Ph.D. thesis, Yale University, 1983.
[10] Yuri, Matijasevich, Enumerable sets are Diophantine,Doklady Akademii Nauka SSSR, vol. 191 (1970), pp. 272–282, Russian.
[11] J. B., Rosser, Extensions of some theorems of Gödel and Church,The Journal of Symbolic Logic, vol. 1 (1936), pp. 87–91.
[12] Dana, Scott, Algebras of sets binumerable in complete extensions of arithmetic,Recursive function theory(J., Dekker, editor), Proceedings of Symposia in Pure Mathematics, vol. V, American Mathematical Society, 1962, pp. 117–122.Google Scholar
[13] Stephen G., Simpson, Degrees of unsolvability: A survey of results, [2], pp. 631–652.
[14] Stephen G., Simpson, Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer, 1999.
[15] Robert, Solovay, Degrees of models of true arithmetic, Circulated preprint, 1982.

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