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Minimal Universes

Name: Minimal Universes
Creator: Friedman, S.D.
Keywords: minimal model of set theory, Mathematics(all), generic extension, backwards Easton forcing, Mathematics - Logic, 16. Peace & justice, 01 natural sciences, inner model, Gödel-Bernays class theory, Inner models, including constructibility, ordinal definability, and core models

Minimal universes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 1994Embargo end date: 01 Jan 1992Publisher:Elsevier BVJournal:Advances in Mathematics, volume 104, pages 59-65 (issn: 0001-8708,

Authors: Friedman, S.D.;

doi: 10.1006/aima.1994.1020 , 10.48550/arxiv.math/9211205

arXiv: http://arxiv.org/abs/math/9211205

Minimal Universes

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Abstract

An inner model M is MINIMAL if there is a class A such that is amenable yet has no transitive proper elementary submodel. We study minimal universes in the context of 0#. For example we prove: If 0# exists then there is an inner model which is minimal and locally generic over L(i.e., every set in the inner model is set-generic over L). This answers a question of Mack Stanley.

Related Organizations

Massachusetts Institute of Technology
United States

Keywords

minimal model of set theory, Mathematics(all), generic extension, backwards Easton forcing, Mathematics - Logic, inner model, Gödel-Bernays class theory, Inner models, including constructibility, ordinal definability, and core models, 0 sharp exists, FOS: Mathematics, Consistency and independence results, Logic (math.LO), club

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