Large cardinals and definable well-orders on the universe

AD Brooke-Taylor

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)


We use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle ♢*κ+ at a proper class of cardinals κ. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.
Translated title of the contributionLarge cardinals and definable well-orders on the universe
Original languageEnglish
Pages (from-to)641 - 654
Number of pages14
JournalJournal of Symbolic Logic
Volume74, issue 2
Publication statusPublished - Jun 2009

Bibliographical note

Publisher: Cornell Univ Library / Duke Univ Press


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