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Arithmetic saturation

Published online by Cambridge University Press:  31 March 2017

By
Roman Kossak
Edited by
Stephen G. Simpson
Stephen G. Simpson
Affiliation:
Pennsylvania State University
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Type
Chapter
Information
Reverse Mathematics 2001 , pp. 296 - 302
Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] Nicholas, Bamber and Henryk, Kotlarski, On interstices of countable arithmetically saturated models of Peano arithmetic,Mathematical Logic Quarterly, vol. 43 (1997), no. 4, pp. 525– 540.
[2] Teresa, Bigorajska, Henryk, Kotlarski, and James H., Schmerl, On regular interstices and selective types in countable arithmetically saturated models of Peano arithmetic,Fundamenta Mathematicae, vol. 158 (1998), no. 2, pp. 125–146.
[3] Andreas R., Blass, Jeffry L., Hirst, and Stephen G., Simpson, Logical analysis of some theorems of combinatorics and topological dynamics,Logic and combinatorics (Arcata, Calif., 1985), Amer.Math. Soc., Providence, RI, 1987, pp. 125–156.
[4] Petr, Hájek and Pavel, Pudlák, Metamathematics of first-order arithmetic, Springer-Verlag, Berlin, 1998, Second printing.
[5] D., Jensen and A., Ehrenfeucht, Some problem in elementary arithmetics,Fundamenta Mathematicae, vol. 92 (1976), no. 3, pp. 223–245.
[6] Richard, Kaye, Models of Peano arithmetic, The Clarendon PressOxford University Press, New York, 1991, Oxford Science Publications.
[7] L. A. S., Kirby and J. B., Paris, Initial segments of models of Peano's axioms,Set theory and hierarchy theory, V (Proc. Third Conf., Bierutowice, 1976), Lecture Notes in Math., vol. 619, Springer, Berlin, 1977, pp. 211–226.
[8] Friederike, Körner, Automorphisms moving all non-algebraic points and an application to NF,The Journal of Symbolic Logic, vol. 63 (1998), no. 3, pp. 815–830.
[9] Roman, Kossak, Automorphisms of recursively saturated models of Peano arithmetic: fixed point sets,Logic Journal of the Interest Group in Pure and Applied Logics, vol. 5 (1997), no. 6, pp. 787–794 (electronic).
[10] Roman, Kossak and James H., Schmerl, Arithmetically saturated models of arithmetic,Notre Dame Journal of Formal Logic, vol. 36 (1995), no. 4, pp. 531–546, Special Issue: Models of arithmetic.
[11] Roman, Kossak and James H., Schmerl, The automorphism group of an arithmetically saturated model of Peano arithmetic,Journal of the London Mathematical Society. Second Series, vol. 52 (1995), no. 2, pp. 235–244.
[12] Daniel, Lascar, The small index property and recursively saturated models of Peano arithmetic,Automorphisms of first-order structures, Oxford Univ. Press, New York, 1994, pp. 281– 292.
[13] James, Schmerl, Generic automorphisms and graph coloring, to appear.
[14] Stephen G., Simpson, Subsystems of second order arithmetic, Springer-Verlag, Berlin, 1999.

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