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 language | English |
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Pages (from-to) | 177-226 |
Number of pages | 50 |
Journal | Israel Journal of Mathematics |
Volume | 42 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1982 |