Dominating analytic families

Anastasis Kamburelis

Fundamenta Mathematicae (1998)

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

Abstract

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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.

How to cite

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Kamburelis, 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

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  1. [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. 
  2. [E] E. Ellentuck, A new proof that analytic sets are Ramsey, J. Symbolic Logic 39 (1974), 163-165. Zbl0292.02054
  3. [F] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebras, Vol. 3, North-Holland, 1989, 877-980. 
  4. [GP] F. Galvin and K. Prikry, Borel sets and Ramsey's theorem, J. Symbolic Logic 38 (1973), 193-198. Zbl0276.04003
  5. [J] T. Jech, Set Theory, Academic Press, New York, 1978. 
  6. [K] A. S. Kechris, Classical Descriptive Set Theory, Springer, New York, 1995. 
  7. [RS] A. Rosłanowski and S. Shelah, Simple forcing notions and forcing axioms, preprint. Zbl0952.03061
  8. [Sh] S. Shelah, How special are Cohen and Random forcings, Israel J. Math. 88 (1994), 159-174. Zbl0815.03031
  9. [S] J. Silver, Every analytic set is Ramsey, J. Symbolic Logic 35 (1970), 60-64. Zbl0216.01304

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