Countable Length Everywhere Club Uniformization

Journal of Symbolic Logic 88 (4):1556-1572 (2023)
  Copy   BIBTEX


Assume $\mathsf {ZF} + \mathsf {AD}$ and all sets of reals are Suslin. Let $\Gamma $ be a pointclass closed under $\wedge $, $\vee $, $\forall ^{\mathbb {R}}$, continuous substitution, and has the scale property. Let $\kappa = \delta (\Gamma )$ be the supremum of the length of prewellorderings on $\mathbb {R}$ which belong to $\Delta = \Gamma \cap \check \Gamma $. Let $\mathsf {club}$ denote the collection of club subsets of $\kappa $. Then the countable length everywhere club uniformization holds for $\kappa $ : For every relation $R \subseteq {}^{<{\omega _1}}\kappa \times \mathsf {club}$ with the property that for all $\ell \in {}^{<{\omega _1}}\kappa $ and clubs $C \subseteq D \subseteq \kappa $, $R(\ell,D)$ implies $R(\ell,C)$, there is a uniformization function $\Lambda : \mathrm {dom}(R) \rightarrow \mathsf {club}$ with the property that for all $\ell \in \mathrm {dom}(R)$, $R(\ell,\Lambda (\ell ))$. In particular, under these assumptions, for all $n \in \omega $, $\boldsymbol {\delta }^1_{2n + 1}$ satisfies the countable length everywhere club uniformization.



    Upload a copy of this work     Papers currently archived: 92,168

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Winning strategies in club games and their applications.Bernhard König - 2011 - Mathematical Logic Quarterly 57 (1):19-26.
The club principle and the distributivity number.Heike Mildenberger - 2011 - Journal of Symbolic Logic 76 (1):34 - 46.
Countable Fréchetα 1-spaces may be first countable.Alan Dow & Juris Stepräns - 1992 - Archive for Mathematical Logic 32 (1):33-50.
Sticks and clubs.Sakaé Fuchino, Saharon Shelah & Lajos Soukup - 1997 - Annals of Pure and Applied Logic 90 (1-3):57-77.
Π 2 1 -Logic and uniformization in the analytical hierarchy.J. P. Ressayre - 1989 - Archive for Mathematical Logic 28 (2):99-117.
The γ-borel conjecture.Arnold W. Miller - 2005 - Archive for Mathematical Logic 44 (4):425-434.
Random generations of the countable random graph.Su Gao & A. Vershik - 2006 - Annals of Pure and Applied Logic 143 (1-3):79-86.
Uniformization principles.Alan H. Mekler & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (2):441-459.
The computational strengths of α-tape infinite time Turing machines.Benjamin Rin - 2014 - Annals of Pure and Applied Logic 165 (9):1501-1511.


Added to PP

10 (#1,197,378)

6 months
7 (#437,422)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

William Chan
University of Manchester

Citations of this work

No citations found.

Add more citations

References found in this work

A Characterization of Generalized Příkrý Sequences.Gunter Fuchs - 2005 - Archive for Mathematical Logic 44 (8):935-971.

Add more references