On extending automorphisms of models of Peano Arithmetic
Kossak, Roman ; Kotlarski, Henryk
Fundamenta Mathematicae, Tome 149 (1996), p. 245-263 / Harvested from The Polish Digital Mathematics Library

Continuing the earlier research in [10] we give some information on extending automorphisms of models of PA to end extensions and cofinal extensions.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:212122
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     title = {On extending automorphisms of models of Peano Arithmetic},
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     volume = {149},
     year = {1996},
     pages = {245-263},
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Kossak, Roman; Kotlarski, Henryk. On extending automorphisms of models of Peano Arithmetic. Fundamenta Mathematicae, Tome 149 (1996) pp. 245-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i3p245bwm/

[00000] [1] A. Ehrenfeucht, Discernible elements in models of Peano arithmetic, J. Symbolic Logic 38 (1973), 291-292. | Zbl 0279.02036

[00001] [2] H. Gaifman, A note on models and submodels of arithmetic, in: Conference in Mathematical Logic, London '70, W. Hodges (ed.), Lecture Notes in Math. 255, Springer, 1972, 128-144.

[00002] [3] H. Gaifman, Models and types of Peano's Arithmetic, Ann. Math. Logic 9 (1976), 223-306. | Zbl 0332.02058

[00003] [4] P. Hájek and P. Pudlák, Metamathematics of First-Order Arithmetic, Perspectives in Math. Logic, Springer, 1993. | Zbl 0781.03047

[00004] [5] W. Hodges, Model Theory, Encyclopedia Math. Appl. 42, Cambridge University Press, 1993.

[00005] [6] R. Kaye, Models of Peano Arithmetic, Oxford Logic Guides 15, Oxford University Press, 1991.

[00006] [7] R. Kaye, A Galois correspondence for countable recursively saturated models of Peano arithmetic, in: R. Kaye and D. Macpherson (eds.), Automorphisms of First Order Structures, Oxford University Press, 1994, 293-312. | Zbl 0824.03015

[00007] [8] R. Kaye, R. Kossak and H. Kotlarski, Automorphisms of recursively saturated models of arithmetic, Ann. Pure Appl. Logic 55 (1991), 67-91. | Zbl 0748.03023

[00008] [9] L. Kirby, Initial segments in models of Peano Arithmetic, Ph.D. Thesis, University of Manchester, 1977.

[00009] [10] R. Kossak and H. Kotlarski, Results on automorphisms of recursively saturated models of PA, Fund. Math. 129 (1988), 9-15. | Zbl 0662.03027

[00010] [11] R. Kossak, H. Kotlarski and J. Schmerl, On maximal subgroups of the automorphism group of a countable recursively saturated models of PA, Ann. Pure Appl. Logic 65 (1993), 125-148. | Zbl 0796.03043

[00011] [12] R. Kossak and J. Schmerl, Minimal satisfaction classes with an application to rigid models of Peano Arithmetic, Notre Dame J. Formal Logic 32 (1991), 392-398. | Zbl 0748.03024

[00012] [13] R. Kossak and J. Schmerl, The automorphism group of an arithmetically saturated model of Peano arithmetic, J. London Math. Soc., to appear. | Zbl 0905.03024

[00013] [14] H. Kotlarski, On elementary cuts in recursively saturated models of arithmetic, Fund. Math. 120 (1984), 205-222. | Zbl 0572.03016

[00014] [15] H. Kotlarski, Automorphisms of countable recursively saturated models of Arithmetic: a survey, Notre Dame J. Formal Logic, submitted. | Zbl 0848.03015

[00015] [16] H. Kotlarski, Addition to the Rosser's Theorem, J. Symbolic Logic, submitted. | Zbl 0848.03030

[00016] [17] D. Lascar, Automorphism group of a recursively saturated model of Peano Arithmetic, in: R. Kaye and D. Macpherson (eds.), Automorphisms of First Order Structures, Oxford University Press, 1994, 281-292. | Zbl 0824.03014

[00017] [18] C. Smoryński, The Incompleteness Theorems, in: J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, 1977, 821-865.

[00018] [19] C. Smoryński, Elementary extensions of recursively saturated models of arithmetic, Notre Dame J. Formal Logic 22 (1981), 193-203. | Zbl 0503.03032

[00019] [20] C. Smoryński and J. Stavi, Cofinal extensions preserve recursive saturation, in: Model Theory of Algebra and Arithmetic, L. Pacholski et al. (eds.), Lecture Notes in Math. 834, Springer, 1981, 338-345.