Better quasi-orders for uncountable cardinals

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

We generalize the theory of Nash-Williams on well quasi-orders and better quasi-orders and later results to uncountable cardinals. We find that the first cardinal κ for which some natural quasi-orders are κ-well-ordered, is a (specific) mild large cardinal. Such quasi-orders are[InlineMediaObject not available: see fulltext.] (the class of orders which are the union of ≦λ scattered orders) ordered by embeddability and the (graph theoretic) trees under embeddings taking edges to edges (rather than to passes).

Original languageEnglish
Pages (from-to)177-226
Number of pages50
JournalIsrael Journal of Mathematics
Volume42
Issue number3
DOIs
StatePublished - Sep 1982

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