In the author's 2012 paper, the V-definable Stable Core 𝕊 = (L[S],S) was introduced. It was shown that V is generic over 𝕊 (for 𝕊-definable dense classes), each V-definable club contains an 𝕊-definable club, and the same holds with 𝕊 replaced by (HOD,S), where HOD denotes Gödel's inner model of hereditarily ordinal-definable sets. In the present article we extend this to models of class theory by introducing the V-definable Enriched Stable Core 𝕊* = (L[S*],S*). As an application we obtain the rigidity of 𝕊* for all embeddings which are "constructible from V". Moreover, any "V-constructible" club contains an "𝕊*-constructible" club. This also applies to the model (HOD,S*), and therefore we conclude that, relative to a V-definable predicate, HOD is rigid for V-constructible embeddings.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-12-2015,
author = {Sy-David Friedman},
title = {The enriched stable core and the relative rigidity of HOD},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {1-12},
zbl = {06622323},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-12-2015}
}
Sy-David Friedman. The enriched stable core and the relative rigidity of HOD. Fundamenta Mathematicae, Tome 233 (2016) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-12-2015/