Analytic determinacy and 0# A forcing-free proof of Harrington’s theorem

• Autorzy: Ramez L. Sami
• Języki publikacji: EN

Abstrakty

EN

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 $0^#$.

Kategorie tematyczne

• 03E60: Determinacy principles
• 03D55: Hierarchies
• 03E55: Large cardinals
• 03D60: Computability and recursion theory on ordinals, admissible sets, etc.
• 03E15: Descriptive set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 160
• Numer: 2
• Strony: 153-159

Daty

otrzymano

1997-12-10

poprawiono

1998-09-20

Twórcy

autor

Ramez L. Sami

• UFR de Mathématiques, Université Paris 7, 75251 Paris Cedex 05, France

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