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
Institute of Mathematics, Agricultural and Pedagogical University (WSRP), Orlicz-Dreszera 19/21, 08-110 Siedlce, Poland
Bibliografia
[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 $IΣ_ n$, 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv160i1p27bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.