Examples for Souslin forcing

Haim Judah; Andrzej Rosłanowski; Saharon Shelah

Fundamenta Mathematicae (1994)

  • Volume: 144, Issue: 1, page 23-42
  • ISSN: 0016-2736

Abstract

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We give several examples of Souslin forcing notions. For instance, we show that there exists a proper analytical forcing notion without ccc and with no perfect set of incompatible elements, we give an example of a Souslin ccc partial order without the Knaster property, and an example of a totally nonhomogeneous Souslin forcing notion.

How to cite

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Judah, Haim, Rosłanowski, Andrzej, and Shelah, Saharon. "Examples for Souslin forcing." Fundamenta Mathematicae 144.1 (1994): 23-42. <http://eudml.org/doc/212013>.

@article{Judah1994,
abstract = {We give several examples of Souslin forcing notions. For instance, we show that there exists a proper analytical forcing notion without ccc and with no perfect set of incompatible elements, we give an example of a Souslin ccc partial order without the Knaster property, and an example of a totally nonhomogeneous Souslin forcing notion.},
author = {Judah, Haim, Rosłanowski, Andrzej, Shelah, Saharon},
journal = {Fundamenta Mathematicae},
keywords = {countable chain condition; Souslin forcing; Knaster property; totally nonhomogeneous Souslin forcing; Souslin partial ordering},
language = {eng},
number = {1},
pages = {23-42},
title = {Examples for Souslin forcing},
url = {http://eudml.org/doc/212013},
volume = {144},
year = {1994},
}

TY - JOUR
AU - Judah, Haim
AU - Rosłanowski, Andrzej
AU - Shelah, Saharon
TI - Examples for Souslin forcing
JO - Fundamenta Mathematicae
PY - 1994
VL - 144
IS - 1
SP - 23
EP - 42
AB - We give several examples of Souslin forcing notions. For instance, we show that there exists a proper analytical forcing notion without ccc and with no perfect set of incompatible elements, we give an example of a Souslin ccc partial order without the Knaster property, and an example of a totally nonhomogeneous Souslin forcing notion.
LA - eng
KW - countable chain condition; Souslin forcing; Knaster property; totally nonhomogeneous Souslin forcing; Souslin partial ordering
UR - http://eudml.org/doc/212013
ER -

References

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  1. [Ba] 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. [BJ] J. Bagaria and H. Judah, Amoeba forcing, Suslin absoluteness and additivity of measure, in: Set Theory of the Continuum, H. Judah, W. Just and H. Woodin (eds.), Math. Sci. Res. Inst. Publ. 26, Springer, 1992, 155-173. Zbl0781.03038
  3. [BaJ] T. Bartoszyński and H. Judah, Jumping with random reals, to appear. Zbl0711.03021
  4. [Je] T. Jech, Set Theory, Academic Press, New York, 1978. 
  5. [Je1] T. Jech, Multiple Forcing, Cambridge Tracts in Math. 88, Cambridge Univ. Press, 1986. 
  6. [JR] H. Judah and A. Rosłanowski, On Shelah's amalgamation, in: Set Theory of the Reals, Proc. Bar-Ilan Univ., 1991, Israel Math. Conf. Proc. 6, Bar-Ilan Univ., 1993, 385-414. Zbl0828.03021
  7. [JS1] H. Judah and S. Shelah, Souslin forcing, J. Symbolic Logic 53 (1988), 1188-1207. 
  8. [JS2] H. Judah and S. Shelah, Martin's axioms, measurability and equiconsistency results, ibid. 54 (1989), 78-94. 
  9. [Ra] J. Raisonnier, A mathematical proof of S. Shelah's theorem on the measure problem and related results, Israel J. Math. 48 (1984), 48-56. Zbl0596.03056
  10. [Ro] J. Roitman, Adding a random or a Cohen real: topological consequences and the effect on Martin's axiom, Fund. Math. 103 (1979), 47-60. Zbl0442.03034
  11. [Sh] S. Shelah, Can you take Solovay's inaccessible away?, Israel J. Math. 48 (1984), 1-47. Zbl0596.03055
  12. [Sh1] S. Shelah, Vive la Différence I: nonisomorphism of ultrapowers of countable models, in: Set Theory of the Continuum, H. Judah, W. Just and H. Woodin (eds.), Math. Sci. Res. Inst. Publ. 26, Springer, 1992, 357-405. Zbl0789.03035
  13. [Sh2] S. Shelah, Proper and Improper Forcing, in preparation. 
  14. [Ta] M. Talagrand, Compacts de fonctions mesurables et filtres non mesurables, Studia Math. 67 (1980), 13-43. Zbl0435.46023
  15. [To] S. Todorčević, Two examples of Borel partially ordered sets with the countable chain condition, Proc. Amer. Math. Soc. 112 (1991), 1125-1128. Zbl0727.03030

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