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Part of 1975 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1975_1

Source: Set Theory

12/30/2008
Show that there exists a tournament (T,→) (T,\rightarrow) of cardinality ℵ1 \aleph_1 containing no transitive subtournament of size ℵ1 \aleph_1. ( A structure (T,→) (T,\rightarrow) is a <spanclass=′latex−italic′>tournament</span> <span class='latex-italic'>tournament</span> if → \rightarrow is a binary, irreflexive, asymmetric and trichotomic relation. The tournament (T,→) (T,\rightarrow) is transitive if → \rightarrow is transitive, that is, if it orders T T.) A. Hajnal
advanced fieldsadvanced fields unsolvedset theoryreal analysis