The enriched stable core and the relative rigidity of HOD

• Autorzy: Sy-David Friedman
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E45: Inner models, including constructibility, ordinal definability, and core models
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 235
• Numer: 1
• Strony: 1-12

Daty

wydano

2016

Twórcy

autor

Sy-David Friedman

• Kurt Gödel Research Center, Währinger Strasse 25, 1090 Wien, Austria

Identyfikatory

DOI

10.4064/fm170-12-2015