# Goldstern–Judah–Shelah preservation theorem for countable support iterations

Fundamenta Mathematicae (1994)

- Volume: 144, Issue: 1, page 55-72
- ISSN: 0016-2736

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topRepický, Miroslav. "Goldstern–Judah–Shelah preservation theorem for countable support iterations." Fundamenta Mathematicae 144.1 (1994): 55-72. <http://eudml.org/doc/212015>.

@article{Repický1994,

abstract = {[1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362. [5] H. Judah and M. Repický, No random reals in countable support iterations, preprint. [6] H. Judah and S. Shelah, The Kunen-Miller chart (Lebesgue measure, the Baire property, Laver reals and preservation theorems for forcing), J. Symbolic Logic 55 (1990), 909-927. [7] A. W. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93-114. [8] J. Pawlikowski, Why Solovay real produces Cohen real, J. Symbolic Logic 51 (1986), 957-968. [9] J. Raisonnier and J. Stern, The strength of measurability hypotheses, Israel J. Math. 50 (1985), 337-349. [10] M. Repický, Properties of measure and category in generalized Cohen’s and Silver’s forcing, Acta Univ. Carol. - Math. Phys. 28 (1987), 101-115. [11] S. Shelah, Proper Forcing, Springer, Berlin, 1984. [12] J. Truss, Sets having caliber $ℵ_1$, in: Logic Colloquium 76, Stud. Logic Found. Math. 87, North-Holland, 1977, 595-612.},

author = {Repický, Miroslav},

journal = {Fundamenta Mathematicae},

keywords = {countable support iterated forcing; proper forcing; preservation theorem for iterated forcing; countable support iteration; preservation theorem; iterated forcing; -bounding property; -bounding property},

language = {eng},

number = {1},

pages = {55-72},

title = {Goldstern–Judah–Shelah preservation theorem for countable support iterations},

url = {http://eudml.org/doc/212015},

volume = {144},

year = {1994},

}

TY - JOUR

AU - Repický, Miroslav

TI - Goldstern–Judah–Shelah preservation theorem for countable support iterations

JO - Fundamenta Mathematicae

PY - 1994

VL - 144

IS - 1

SP - 55

EP - 72

AB - [1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362. [5] H. Judah and M. Repický, No random reals in countable support iterations, preprint. [6] H. Judah and S. Shelah, The Kunen-Miller chart (Lebesgue measure, the Baire property, Laver reals and preservation theorems for forcing), J. Symbolic Logic 55 (1990), 909-927. [7] A. W. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93-114. [8] J. Pawlikowski, Why Solovay real produces Cohen real, J. Symbolic Logic 51 (1986), 957-968. [9] J. Raisonnier and J. Stern, The strength of measurability hypotheses, Israel J. Math. 50 (1985), 337-349. [10] M. Repický, Properties of measure and category in generalized Cohen’s and Silver’s forcing, Acta Univ. Carol. - Math. Phys. 28 (1987), 101-115. [11] S. Shelah, Proper Forcing, Springer, Berlin, 1984. [12] J. Truss, Sets having caliber $ℵ_1$, in: Logic Colloquium 76, Stud. Logic Found. Math. 87, North-Holland, 1977, 595-612.

LA - eng

KW - countable support iterated forcing; proper forcing; preservation theorem for iterated forcing; countable support iteration; preservation theorem; iterated forcing; -bounding property; -bounding property

UR - http://eudml.org/doc/212015

ER -

## References

top- [1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. Zbl0538.03042
- [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. Zbl0787.03036
- [3] D. H. Fremlin, Cichoń's diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp.
- [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362.
- [5] H. Judah and M. Repický, No random reals in countable support iterations, preprint. Zbl0838.03039
- [6] H. Judah and S. Shelah, The Kunen-Miller chart (Lebesgue measure, the Baire property, Laver reals and preservation theorems for forcing), J. Symbolic Logic 55 (1990), 909-927. Zbl0718.03037
- [7] A. W. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93-114. Zbl0472.03040
- [8] J. Pawlikowski, Why Solovay real produces Cohen real, J. Symbolic Logic 51 (1986), 957-968. Zbl0622.03036
- [9] J. Raisonnier and J. Stern, The strength of measurability hypotheses, Israel J. Math. 50 (1985), 337-349. Zbl0602.03012
- [10] M. Repický, Properties of measure and category in generalized Cohen's and Silver's forcing, Acta Univ. Carol. - Math. Phys. 28 (1987), 101-115. Zbl0646.03047
- [11] S. Shelah, Proper Forcing, Springer, Berlin, 1984.
- [12] J. Truss, Sets having caliber ${\aleph}_{1}$, in: Logic Colloquium 76, Stud. Logic Found. Math. 87, North-Holland, 1977, 595-612.

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