The real core model and its scales

Annals of Pure and Applied Logic 72 (3):213-289 (1995)
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Abstract

This paper introduces the real core model K() and determines the extent of scales in this inner model. K() is an analog of Dodd-Jensen's core model K and contains L(), the smallest inner model of ZF containing the reals R. We define iterable real premice and show that Σ1∩() has the scale property when vR AD. We then prove the following Main Theorem: ZF + AD + V = K() DC. Thus, we obtain the Corollary: If ZF + AD +()L() is consistent, then ZF + AD + DC + α < ω2 -AD is also consistent

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10.1016/0168-0072(94)00023-v

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References found in this work

The core model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
An extension of borel determinacy.Donald A. Martin - 1990 - Annals of Pure and Applied Logic 49 (3):279-293.
The equivalence of determinacy and iterated sharps.Derrick Albert Dubose - 1990 - Journal of Symbolic Logic 55 (2):502-525.

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