On extending automorphisms of models of Peano Arithmetic

Roman Kossak; Henryk Kotlarski

Fundamenta Mathematicae (1996)

  • Volume: 149, Issue: 3, page 245-263
  • ISSN: 0016-2736

Abstract

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

How to cite

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Kossak, Roman, and Kotlarski, Henryk. "On extending automorphisms of models of Peano Arithmetic." Fundamenta Mathematicae 149.3 (1996): 245-263. <http://eudml.org/doc/212122>.

@article{Kossak1996,
abstract = {Continuing the earlier research in [10] we give some information on extending automorphisms of models of PA to end extensions and cofinal extensions.},
author = {Kossak, Roman, Kotlarski, Henryk},
journal = {Fundamenta Mathematicae},
keywords = {models of arithmetic; recursively saturated models of Peano arithmetic; end extensions; cofinal extensions; automorphism extension property},
language = {eng},
number = {3},
pages = {245-263},
title = {On extending automorphisms of models of Peano Arithmetic},
url = {http://eudml.org/doc/212122},
volume = {149},
year = {1996},
}

TY - JOUR
AU - Kossak, Roman
AU - Kotlarski, Henryk
TI - On extending automorphisms of models of Peano Arithmetic
JO - Fundamenta Mathematicae
PY - 1996
VL - 149
IS - 3
SP - 245
EP - 263
AB - Continuing the earlier research in [10] we give some information on extending automorphisms of models of PA to end extensions and cofinal extensions.
LA - eng
KW - models of arithmetic; recursively saturated models of Peano arithmetic; end extensions; cofinal extensions; automorphism extension property
UR - http://eudml.org/doc/212122
ER -

References

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  2. [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. 
  3. [3] H. Gaifman, Models and types of Peano's Arithmetic, Ann. Math. Logic 9 (1976), 223-306. Zbl0332.02058
  4. [4] P. Hájek and P. Pudlák, Metamathematics of First-Order Arithmetic, Perspectives in Math. Logic, Springer, 1993. Zbl0781.03047
  5. [5] W. Hodges, Model Theory, Encyclopedia Math. Appl. 42, Cambridge University Press, 1993. 
  6. [6] R. Kaye, Models of Peano Arithmetic, Oxford Logic Guides 15, Oxford University Press, 1991. 
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  9. [9] L. Kirby, Initial segments in models of Peano Arithmetic, Ph.D. Thesis, University of Manchester, 1977. 
  10. [10] R. Kossak and H. Kotlarski, Results on automorphisms of recursively saturated models of PA, Fund. Math. 129 (1988), 9-15. Zbl0662.03027
  11. [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. Zbl0796.03043
  12. [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. Zbl0748.03024
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  14. [14] H. Kotlarski, On elementary cuts in recursively saturated models of arithmetic, Fund. Math. 120 (1984), 205-222. Zbl0572.03016
  15. [15] H. Kotlarski, Automorphisms of countable recursively saturated models of Arithmetic: a survey, Notre Dame J. Formal Logic, submitted. Zbl0848.03015
  16. [16] H. Kotlarski, Addition to the Rosser's Theorem, J. Symbolic Logic, submitted. Zbl0848.03030
  17. [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. Zbl0824.03014
  18. [18] C. Smoryński, The Incompleteness Theorems, in: J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, 1977, 821-865. 
  19. [19] C. Smoryński, Elementary extensions of recursively saturated models of arithmetic, Notre Dame J. Formal Logic 22 (1981), 193-203. Zbl0503.03032
  20. [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. 

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