Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published December 1978 | Published
Journal Article Open

The Perfect Set Theorem and Definable Wellorderings of the Continuum

Abstract

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.

Additional Information

© 1979, Association for Symbolic Logic. Received November 15, 1976. Research partially supported by NSF Grant MPS75-07562.

Attached Files

Published - 2273501.pdf

Files

2273501.pdf
Files (183.8 kB)
Name Size Download all
md5:52002e6dadf82c3c03f02937eb8f7a7c
183.8 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024