Geodesic
Analytic determinacy and $0^{\# }$ A forcing-free proof of Harrington’s theorem
Fundamenta Mathematicae, Tome 160 (1999) no. 2, pp. 153-159 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 $0^#$.
DOI : 10.4064/fm-160-2-153-159

Ramez L. Sami 1

1 
@article{10_4064_fm_160_2_153_159,
     author = {Ramez L.  Sami},
     title = {Analytic determinacy and $0^{\# }$ {A} forcing-free proof of {Harrington{\textquoteright}s} theorem},
     journal = {Fundamenta Mathematicae},
     pages = {153--159},
     year = {1999},
     volume = {160},
     number = {2},
     doi = {10.4064/fm-160-2-153-159},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-160-2-153-159/}
}
TY  - JOUR
AU  - Ramez L.  Sami
TI  - Analytic determinacy and $0^{\# }$ A forcing-free proof of Harrington’s theorem
JO  - Fundamenta Mathematicae
PY  - 1999
SP  - 153
EP  - 159
VL  - 160
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-160-2-153-159/
DO  - 10.4064/fm-160-2-153-159
LA  - en
ID  - 10_4064_fm_160_2_153_159
ER  - 
%0 Journal Article
%A Ramez L.  Sami
%T Analytic determinacy and $0^{\# }$ A forcing-free proof of Harrington’s theorem
%J Fundamenta Mathematicae
%D 1999
%P 153-159
%V 160
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-160-2-153-159/
%R 10.4064/fm-160-2-153-159
%G en
%F 10_4064_fm_160_2_153_159
Ramez L.  Sami. Analytic determinacy and $0^{\# }$ A forcing-free proof of Harrington’s theorem. Fundamenta Mathematicae, Tome 160 (1999) no. 2, pp. 153-159. doi: 10.4064/fm-160-2-153-159

Cité par Sources :