The downward directed grounds hypothesis and very large cardinals

Toshimichi Usuba*

*この研究の対応する著者

研究成果: Article査読

13 被引用数 (Scopus)

抄録

A transitive model M of ZFC is called a ground if the universe V is a set forcing extension of M. We show that the grounds ofV are downward set-directed. Consequently, we establish some fundamental theorems on the forcing method and the set-theoretic geology. For instance, (1) the mantle, the intersection of all grounds, must be a model of ZFC. (2) V has only set many grounds if and only if the mantle is a ground. We also show that if the universe has some very large cardinal, then the mantle must be a ground.

本文言語English
論文番号1750009
ジャーナルJournal of Mathematical Logic
17
2
DOI
出版ステータスPublished - 2017 12 1

ASJC Scopus subject areas

  • 論理

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