# Examples for Souslin forcing

Haim Judah; Andrzej Rosłanowski; Saharon Shelah

Fundamenta Mathematicae (1994)

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

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topJudah, 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

top- [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.
- [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
- [BaJ] T. Bartoszyński and H. Judah, Jumping with random reals, to appear. Zbl0711.03021
- [Je] T. Jech, Set Theory, Academic Press, New York, 1978.
- [Je1] T. Jech, Multiple Forcing, Cambridge Tracts in Math. 88, Cambridge Univ. Press, 1986.
- [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
- [JS1] H. Judah and S. Shelah, Souslin forcing, J. Symbolic Logic 53 (1988), 1188-1207.
- [JS2] H. Judah and S. Shelah, Martin's axioms, measurability and equiconsistency results, ibid. 54 (1989), 78-94.
- [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
- [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
- [Sh] S. Shelah, Can you take Solovay's inaccessible away?, Israel J. Math. 48 (1984), 1-47. Zbl0596.03055
- [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
- [Sh2] S. Shelah, Proper and Improper Forcing, in preparation.
- [Ta] M. Talagrand, Compacts de fonctions mesurables et filtres non mesurables, Studia Math. 67 (1980), 13-43. Zbl0435.46023
- [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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