# Dominating analytic families

Fundamenta Mathematicae (1998)

- Volume: 156, Issue: 1, page 73-83
- ISSN: 0016-2736

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topKamburelis, Anastasis. "Dominating analytic families." Fundamenta Mathematicae 156.1 (1998): 73-83. <http://eudml.org/doc/212262>.

@article{Kamburelis1998,

abstract = {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.},

author = {Kamburelis, Anastasis},

journal = {Fundamenta Mathematicae},

keywords = {measure algebra; Cohen algebra; Suslin c.c.c. forcing; distributivity; Suslin forcing; Ellentuck topology; analytic set; unbounded real; Cohen real},

language = {eng},

number = {1},

pages = {73-83},

title = {Dominating analytic families},

url = {http://eudml.org/doc/212262},

volume = {156},

year = {1998},

}

TY - JOUR

AU - Kamburelis, Anastasis

TI - Dominating analytic families

JO - Fundamenta Mathematicae

PY - 1998

VL - 156

IS - 1

SP - 73

EP - 83

AB - 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.

LA - eng

KW - measure algebra; Cohen algebra; Suslin c.c.c. forcing; distributivity; Suslin forcing; Ellentuck topology; analytic set; unbounded real; Cohen real

UR - http://eudml.org/doc/212262

ER -

## References

top- [B] J. Baumgartner, Iterated forcing, in: Surveys in Set Theory, A. R. D. Mathias (ed.), London Math. Soc. Lecture Note Ser. 87, Cambridge Univ. Press, 1983, 1-59.
- [E] E. Ellentuck, A new proof that analytic sets are Ramsey, J. Symbolic Logic 39 (1974), 163-165. Zbl0292.02054
- [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. Zbl0276.04003
- [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. Zbl0952.03061
- [Sh] S. Shelah, How special are Cohen and Random forcings, Israel J. Math. 88 (1994), 159-174. Zbl0815.03031
- [S] J. Silver, Every analytic set is Ramsey, J. Symbolic Logic 35 (1970), 60-64. Zbl0216.01304

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