David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 43 (4):630-634 (1978)
Let Γ be a collection of relations on the reals and let M be a set of reals. We call M a perfect set basis for Γ if every set in Γ with parameters from M which is not totally included in M contains a perfect subset with code in M. A simple elementary proof is given of the following result (assuming mild regularity conditions on Γ and M): If M is a perfect set basis for Γ, the field of every wellordering in Γ is contained in M. An immediate corollary is Mansfield's Theorem that the existence of a Σ 1 2 wellordering of the reals implies that every real is constructible. Other applications and extensions of the main result are also given
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Peter Aczel, Laura Crosilla, Hajime Ishihara, Erik Palmgren & Peter Schuster (2006). Binary Refinement Implies Discrete Exponentiation. Studia Logica 84 (3):361 - 368.
Reinhard Selten (1998). Multistage Game Models and Delay Supergames. Theory and Decision 44 (1):1-36.
George Barmpalias (2010). Relative Randomness and Cardinality. Notre Dame Journal of Formal Logic 51 (2):195-205.
Mitch Rudominer (1999). The Largest Countable Inductive Set is a Mouse Set. Journal of Symbolic Logic 64 (2):443-459.
Ali Enayat (2001). Power-Like Models of Set Theory. Journal of Symbolic Logic 66 (4):1766-1782.
Robert S. Lubarsky & Michael Rathjen (2008). On the Constructive Dedekind Reals. Logic and Analysis 1 (2):131-152.
Vladimir Kanovei (1999). On Non-Wellfounded Iterations of the Perfect Set Forcing. Journal of Symbolic Logic 64 (2):551-574.
Arnold W. Miller (1983). Mapping a Set of Reals Onto the Reals. Journal of Symbolic Logic 48 (3):575-584.
Marcia J. Groszek & Theodore A. Slaman (1998). A Basis Theorem for Perfect Sets. Bulletin of Symbolic Logic 4 (2):204-209.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #445,363 of 1,102,738 )
Recent downloads (6 months)1 ( #296,833 of 1,102,738 )
How can I increase my downloads?