Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We prove the following theorem: Given a⊆ω and $1 ≤ α < ω_1^{CK}$, if for some $η < ℵ_1$ and all u ∈ WO of length η, a is $Σ _α^0(u)$, then a is $Σ_α^0$.} We use this result to give a new, forcing-free, proof of Leo Harrington's theorem: {$Σ_1^1 $-Turing-determinacy implies the existence of $0^{#}$}.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
101-151
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-12-10
poprawiono
1998-09-20
Twórcy
autor
- UFR de Mathématiques, Université Paris 7, 75251 Paris Cedex 05, France, sami@logique.jussieu.fr
autor
Bibliografia
- [Gn] R. O. Gandy, On a problem of Kleene's, Bull. Amer. Math. Soc. 66 (1960), 501-502.
- [Hg] L. A. Harrington, Analytic determinacy and $0^#$, J. Symbolic Logic 43 (1978), 685-693.
- [Hn] J. Harrison, Recursive pseudo-well-orderings, Trans. Amer. Math. Soc. 131 (1968), 526-543.
- [Kn] A. Kanamori, The Higher Infinite, 2nd printing, Springer, Berlin, 1997.
- [Kc] A. S. Kechris, Measure and category in effective descriptive set-theory, Ann. Math. Logic 5 (1973), 337-384.
- [MW] R. Mansfield and G. Weitkamp, Recursive Aspects of Descriptive Set Theory, Oxford Univ. Press, Oxford, 1985.
- [Mr1] D. A. Martin, The axiom of determinacy and reduction principles in the analytical hierarchy, Bull. Amer. Math. Soc. 74 (1968), 687-689.
- [Mr2] D. A. Martin, Measurable cardinals and analytic games, Fund. Math. 66 (1970), 287-291.
- [Ms] Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam, 1980.
- [Sc1] G. E. Sacks, Countable admissible ordinals and hyperdegrees, Adv. Math. 19 (1976), 213-262.
- [Sc2] G. E. Sacks, Higher Recursion Theory, Springer, Berlin, 1990.
- [Sm] R. L. Sami, Questions in descriptive set theory and the determinacy of infinite games, Ph.D. Dissertation, Univ. of California, Berkeley, 1976.
- [Sl] J. Steel, Forcing with tagged trees, Ann. Math. Logic 15 (1978), 55-74.
- [Sr] J. Stern, Evaluation du rang de Borel de certains ensembles, C. R. Acad. Sci. Paris Sér. I 286 (1978), 855-857.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv160i2p101bwm