Dominating analytic families

• Autorzy: Anastasis Kamburelis
• Języki publikacji: EN

Abstrakty

EN

Let A be an analytic family of sequences of sets of integers. We show that either A is dominated or it contains a continuum of almost disjoint sequences. From this we obtain a theorem by Shelah that a Suslin c.c.c. forcing adds a Cohen real if it adds an unbounded real.

Słowa kluczowe

EN

measure algebra; Cohen algebra; Suslin c.c.c. forcing; distributivity

Kategorie tematyczne

• 03E15: Descriptive set theory
• 06E10: Chain conditions, complete algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 156
• Numer: 1
• Strony: 73-83

Daty

wydano

1998

otrzymano

1997-04-10

poprawiono

1997-08-15

Twórcy

autor

Anastasis Kamburelis

• Department of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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• [F] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebras, Vol. 3, North-Holland, 1989, 877-980.
• [GP] F. Galvin and K. Prikry, Borel sets and Ramsey's theorem, J. Symbolic Logic 38 (1973), 193-198.
• [J] T. Jech, Set Theory, Academic Press, New York, 1978.
• [K] A. S. Kechris, Classical Descriptive Set Theory, Springer, New York, 1995.
• [RS] A. Rosłanowski and S. Shelah, Simple forcing notions and forcing axioms, preprint.
• [Sh] S. Shelah, How special are Cohen and Random forcings, Israel J. Math. 88 (1994), 159-174.
• [S] J. Silver, Every analytic set is Ramsey, J. Symbolic Logic 35 (1970), 60-64.