Affordable Access

Publisher Website

The real core model and its scales

Authors
Journal
Annals of Pure and Applied Logic
0168-0072
Publisher
Elsevier
Publication Date
Volume
72
Issue
3
Identifiers
DOI: 10.1016/0168-0072(94)00023-v

Abstract

Abstract This paper introduces the real core model K( R ) and determines the extent of scales in this inner model. K( R ) is an analog of Dodd-Jensen's core model K and contains L( R ), the smallest inner model of ZF containing the reals R. We define iterable real premice M and show that Σ 1( scM)∩ P ( R ) has the scale property when M vR AD. We then prove the following Main Theorem: ZF + AD + V = K( R ) ⇒ DC. Thus, we obtain the Corollary: If ZF + AD + P ( R )⊈ L( R ) is consistent, then ZF + AD + DC + ∀ α < ω 2 ( α- Π 1 1)- AD R is also consistent.

There are no comments yet on this publication. Be the first to share your thoughts.