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ArticleOriginal scientific text

Title

A partition theorem for α-large sets

Authors 1, 1

Affiliations

  1. Institute of Mathematics, Agricultural and Pedagogical University (WSRP), Orlicz-Dreszera 19/21, 08-110 Siedlce, Poland

Abstract

Working with Hardy hierarchy and the notion of largeness determined by it, we define the notion of a partition of a finite set of natural numbers !$!A=∪_{i

Bibliography

  1. T. Bigorajska, H. Kotlarski and J. Schmerl, On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic, Fund. Math. 158 (1998), 125-146.
  2. C E. A. Cichon, A short proof of two recently discovered independence results using recursion theoretic methods, Proc. Amer. Math. Soc. 87 (1983), 704-706.
  3. W M. V. H. Fairlough and S. S. Wainer, Ordinal complexity of recursive definitions, Inform. and Comput. 99 (1992), 123-153.
  4. R. Graham, B. Rothschild and J. Spencer, Ramsey Theory, 2nd ed., Wiley, 1990.
  5. J. Ketonen and R. Solovay, Rapidly growing Ramsey functions, Ann. of Math. 113 (1981), 267-314.
  6. H. Kotlarski and Z. Ratajczyk, Inductive full satisfaction classes, Ann. Pure Appl. Logic 47 (1990), 199-223.
  7. H. Kotlarski and Z. Ratajczyk, More on induction in the language with a satisfaction class, Z. Math. Logik 36 (1990), 441-454.
  8. W. Pohlers, Proof Theory, Lecture Notes in Math. 1047, Springer, 1989.
  9. Z. Ratajczyk, A combinatorial analysis of functions provably recursive in IΣn, Fund. Math. 130 (1988), 191-213.
  10. Z. Ratajczyk, Subsystems of true arithmetic and hierarchies of functions, Ann. Pure Appl. Logic 64 (1993), 95-152.
  11. R. Sommer, Transfinite induction within Peano arithmetic, ibid. 76 (1995), 231-289.
Fundamenta Mathematicae
1999/160/1
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Pages:
27-37
Main language of publication
English
Received
1998-01-27
Accepted
1998-12-28
Published
1999
Exact and natural sciences