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1998 | 158 | 2 | 125-146
Tytuł artykułu

On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.
Słowa kluczowe
Rocznik
Tom
158
Numer
2
Strony
125-146
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-02-20
poprawiono
1998-04-14
poprawiono
1998-06-02
Twórcy
  • Institute of Mathematics, Agricultural and Pedagogical University, Orlicz-Dreszera 19/21, 08-110 Siedlce, Poland, terebi@wsrp.siedlce.pl
  • Institute of Mathematics, Agricultural and Pedagogical University, Orlicz-Dreszera 19/21, 08-110 Siedlce, Poland, hkl@impan.gov.pl
  • Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269 U.S.A., schmerl@math.uconn.edu
Bibliografia
  • [1] N. Bamber and H. Kotlarski, On interstices in countable arithmetically saturated models of Peano Arithmetic, Math. Logic Quart. 43 (1997), 525-540.
  • [2] T. Bigorajska and H. Kotlarski, A partition theorem for α-large sets, to appear.
  • [3] P. Erdős and R. Rado, A combinatorial theorem, J. London Math. Soc. 25 (1950), 249-255.
  • [4] R. Graham, B. Rothschild and J. Spencer, Ramsey Theory, 2nd ed., Wiley, 1990.
  • [5] A. Grzegorczyk, Some classes of recursive functions, Dissertationes Math. 4 (1953).
  • [6] P. Hájek and P. Pudlák, Metamathematics of First Order Arithmetic, Perspect. Math. Logic, Springer, 1993.
  • [7] R. Kaye, Models of Peano Arithmetic, Oxford Logic Guides, Oxford Univ. Press, 1991.
  • [8] R. Kaye, R. Kossak and H. Kotlarski, Automorphisms of recursively saturated models of arithmetic, Ann. Pure Appl. Logic 55 (1991), 67-91.
  • [9] J. Ketonen and R. Solovay, Rapidly growing Ramsey functions, Ann. of Math. 113 (1981), 267-314.
  • [10] R. Kossak, H. Kotlarski and J. Schmerl, On maximal subgroups of the automorphism group of a countable recursively saturated model of Peano arithmetic, Ann. Pure Appl. Logic 65 (1993), 125-148.
  • [11] R. Kossak and J. Schmerl, The automorphism group of an arithmetically saturated model of Peano arithmetic, J. London Math. Soc. (2) 52 (1995), 235-244.
  • [12] R. Kossak and J. Schmerl, Arithmetically saturated models of arithmetic, Notre Dame J. Formal Logic 36 (1995), 531-546.
  • [13] H. Kotlarski, On elementary cuts in recursively saturated models of arithmetic, Fund. Math. 120 (1984), 205-222.
  • [14] H. Kotlarski, Automorphisms of countable recursively saturated models of PA: a survey, Notre Dame J. Formal Logic 36 (1995), 505-518.
  • [15 H. Kotlarski and R. Kaye, Automorphisms of models of True Arithmetic: recognising some basic open subgroups, ibid. 35 (1994), 1-14.
  • [16] H. Kotlarski and Z. Ratajczyk, Inductive full satisfaction classes, Ann. Pure Appl. Logic 47 (1990), 199-223.
  • [17] H. Kotlarski and Z. Ratajczyk, More on induction in the language with a satisfaction class, Z. Math. Logik 36 (1990), 441-454.
  • [18] W. Pohlers, Proof Theory, Lecture Notes in Math. 1047, Springer, 1989.
  • [19] Z. Ratajczyk, A combinatorial analysis of functions provably recursive in $IΣ_n$, Fund. Math. 130 (1988), 191-213.
  • [20] Z. Ratajczyk, Subsystems of true arithmetic and hierarchies of functions, Ann. Pure Appl. Logic 64 (1993), 95-152.
  • [21] H. Rogers, The Theory of Recursive Functions and Effective Computability, McGraw-Hill, 1967.
  • [22] D. Scott, Algebras of sets binumerable in complete extensions of arithmetic, in: Recursive Function Theory, Amer. Math. Soc., Providence, 1962, 117-121.
  • [23] R. Sommer, Transfinite induction within Peano arithmetic, Ann. Pure Appl. Logic 76 (1995), 231-289.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv158i2p125bwm
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