In:
Journal of Symbolic Logic, Cambridge University Press (CUP), Vol. 67, No. 2 ( 2002-06), p. 721-736
Abstract:
In this paper we shall repair some errors and fill some gaps in the inner model theory of [2]. The problems we shall address affect some quite basic definitions and proofs. We shall be concerned with condensation properties of canonical inner models constructed from coherent sequences of extenders as in [2]. Condensation results have the general form: if x is definable in a certain way over a level , then either x ∈ , or else from x we can reconstruct in a simple way. The first condensation property considered in [2] is the initial segment condition , or ISC. In section 1 we show that the version of this condition described in [2] is too strong, in that no coherent in which the extenders are indexed in the manner of [2], and which is such that L [ ] satisfies the mild large cardinal hypothesis that there is a cardinal which is strong past a measurable, can satisfy the full ISC of [2] . It follows that the coherent sequences constructed in [2] do not satisfy the ISC of [2] . We shall describe the weaker ISC which these sequences do satisfy, and indicate the small changes in the arguments of [2] this new condition requires.
Type of Medium:
Online Resource
ISSN:
0022-4812
,
1943-5886
DOI:
10.2178/jsl/1190150106
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2002
detail.hit.zdb_id:
2010607-5
SSG:
5,1
SSG:
17,1
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