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Alcune osservazioni sul linguaggio L ( Q 1 )

Aroldo Goretti (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An existence theorem for 1-atomic standard models of L ω ω ( Q 1 ) (more weak than usual “atomic models”) and applications of L ω ω ( Q 1 ) to L ω ω are the results of this note.

Combinatorics and quantifiers

Jaroslav Nešetřil (1996)

Commentationes Mathematicae Universitatis Carolinae

Let I m be the set of subsets of I of cardinality m . Let f be a coloring of I m and g a coloring of I m . We write f g if every f -homogeneous H I is also g -homogeneous. The least m such that f g for some f : I m k is called the k -width of g and denoted by w k ( g ) . In the first part of the paper we prove the existence of colorings with high k -width. In particular, we show that for each k > 0 and m > 0 there is a coloring g with w k ( g ) = m . In the second part of the paper we give applications of wide colorings in the theory of generalized quantifiers....

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