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Magidor, Menachem

Precipitous ideals and \(\sum^1_4\) sets. (English) Zbl 0445.03023

Isr. J. Math. 35, 109-134 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0445.03023

Cited in 11 Documents

MSC:

03E15 Descriptive set theory

Keywords:

Lebesgue-measurable sets; Baire property; precipitous ideal; generic ultrapower; measurable cardinal; perfect subset

Citations:

Zbl 0295.02039
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Full Text: DOI

References:

[1] Gaifman, H., Elementary embeddings of set theory, Proc. Symposia in Pure Math.13 (2) (1974), Providence, RI: Amer. Math. Soc., Providence, RI · Zbl 0342.02042
[2] Galvin, E.; Jech, T. J.; Magidor, M., An ideal game, J. Symbolic Logic, 43, 284-292 (1978) · Zbl 0397.03036 · doi:10.2307/2272827
[3] L. Harrington,Analytic determinacy and 0^#, J. Symbolic Logic, to appear. · Zbl 0398.03039
[4] Jech, T. J., Set Theory (1978), New York: Academic Press, New York · Zbl 0419.03028
[5] Jech, T. J.; Prikry, K., Ideals on sets and the power set operation, Bull. Amer. Math. Soc., 82, 593-595 (1976) · Zbl 0339.02060 · doi:10.1090/S0002-9904-1976-14121-3
[6] T. J. Jech, M. Magidor, W. Mitchell and K. Prikry,On precipitous ideals. J. Symbolic Logic, to appear. · Zbl 0437.03026
[7] Kanamori, A.; Magidor, M., The evolution of large cardinal axioms in set theory, Higher Set Theory, 99-275 (1978), Berlin, Heidelberg, New York: Springer-Verlag, Berlin, Heidelberg, New York · Zbl 0381.03038 · doi:10.1007/BFb0103104
[8] Kunen, K., Some applications of interated ultrapowers in set theory, Ann. Math. Logic, 1, 179-227 (1970) · Zbl 0236.02053 · doi:10.1016/0003-4843(70)90013-6
[9] Kunen, K., Saturated ideals, J. Symbolic Logic, 43, 65-76 (1978) · Zbl 0395.03031 · doi:10.2307/2271949
[10] Kuratowski, C., Topologia (1958), Warsaw: Panstowe Wydawnictwo Naukowe, Warsaw · Zbl 0078.14603
[11] Levy, A.; Solovay, R. M., Measurable cardinals and the continuum hypothesis, Israel J. Math, 5, 234-248 (1967) · Zbl 0289.02044
[12] Łos, J., Quelques remarques théorèmes et problèmes sur les classes definables d’algèbres, Mathematical Interpretations of Formal Systems, 98-113 (1955), Amsterdam: North-Holland, Amsterdam · Zbl 0068.24401
[13] Mansfield, R., A Souslin operation for II_1^2134-1 · Zbl 0295.02039
[14] Martin, D. A.; Solovay, R. M., A basis theorem for Σ_1^3134-2 · Zbl 0176.27603 · doi:10.2307/1970813
[15] Shoenfield, J. R., Mathematical Logic (1967), Reading, Menlo Park, London, Don Mills: Addison-Wesley, Reading, Menlo Park, London, Don Mills · Zbl 0155.01102
[16] Shoenfield, J. R., Uramified forcing, Proc. Symposia in Pure Math.13 (1), 357-381 (1971), Providence, RI: Amer. Math. Soc., Providence, RI · Zbl 0245.02056
[17] Solovay, R. M., A non constructible △_1^3134-3 · Zbl 0161.00704 · doi:10.2307/1994631
[18] Solovay, R. M., The cardinality of Σ_1^2134-4
[19] Solovay, R. M., A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math., 92, 1-56 (1970) · Zbl 0207.00905 · doi:10.2307/1970696
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