The enriched stable core and the relative rigidity of HOD

Sy-David Friedman. "The enriched stable core and the relative rigidity of HOD." Fundamenta Mathematicae 235.1 (2016): 1-12. <http://eudml.org/doc/286597>.

@article{Sy2016,
abstract = {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.},
author = {Sy-David Friedman},
journal = {Fundamenta Mathematicae},
keywords = {stable core; infinitary logic; rigidity; HOD},
language = {eng},
number = {1},
pages = {1-12},
title = {The enriched stable core and the relative rigidity of HOD},
url = {http://eudml.org/doc/286597},
volume = {235},
year = {2016},
}

TY - JOUR
AU - Sy-David Friedman
TI - The enriched stable core and the relative rigidity of HOD
JO - Fundamenta Mathematicae
PY - 2016
VL - 235
IS - 1
SP - 1
EP - 12
AB - 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.
LA - eng
KW - stable core; infinitary logic; rigidity; HOD
UR - http://eudml.org/doc/286597
ER -