Abstract.
We continue developing the general theory of forcing notions built with the use of norms on possibilities, this time concentrating on ccc forcing notions and classifying them.
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Bartoszyński, T., Judah, H.: Set Theory: On the Structure of the Real Line. A K Peters, Wellesley, Massachusetts, 1995
Brendle, J., Judah, H.: Perfect sets of random reals. Israel J. Math. 83, 153–176 (1993)
Goldstern, M., Judah, H.: Iteration of Souslin Forcing, Projective Measurability and the Borel Conjecture. Israel J. Math. 78, 335–362 (1992)
Hall, P.: On representatives of subsets. J. London Math. Soc. 10, 26–30 (1935)
Ihoda, J., (Haim Judah) Shelah, S.: Souslin forcing. J. Symbolic Logic 53, 1188–1207 (1988)
Judah, H., Rosłanowski, A.: On Shelah’s Amalgamation. In: Set Theory of the Reals. volume 6 of Israel Math. Conference Proceedings, 1992, pp. 385–414
Judah, H., Rosłanowski, A.: The ideals determined by Souslin forcing notions. Unpublished notes, 1992, math.LO/9905144
Judah, H., Roslanowski, A., Shelah, S.: Examples for Souslin Forcing. Fundamenta Math. 144, 23–42 (1994) math.LO/9310224
Judah, H., Shelah, S.: Baire Property and Axiom of Choice. Israel J. Math. 84, 435–450 (1993) math.LO/9211213
Kechris, A.S., Solecki, S.: Approximation of analytic by Borel sets and definable countable chain conditions. Israel J. Math. 89, 343–356 (1995)
Kunen, K.: Random and Cohen Reals. In: Kunen, K., Vaughan, J.E., (eds.), Handbook of Set–Theoretic Topology. Elsevier Science Publishers BV, 1984, pp. 887–911
Miller, A.W.: Some properties of measure and category. Trans. Am. Math. Soc. 266, 93–114 (1981)
Roitman, J.: More homogeneous almost disjoint families. Algebra Universalis 47, 267–282 (2002)
Roslanowski, A., Shelah, S.: Measured creatures. Israel J. Math. submitted. math.LO/0010070
Roslanowski, A., Shelah, S.: Norms on possibilities I: forcing with trees and creatures. Mem. Am. Math. Soc. 141 (671), (1999) math.LO/9807172
Roslanowski, A., Shelah, S.: Norms on possibilities II: More ccc ideals on 2ω. J. Appl. Anal. 3, 103–127 (1997) math.LO/9703222
Roslanowski, A., Shelah, S.: Norms on possibilities III: strange subsets of the real line. In preparation
Roslanowski, A., Shelah, S.: 446 revisited. F380
Shelah, S.: Properness Without Elementaricity. J. Appl. Anal. Accepted math.LO/ 9712283
Shelah, S.: Non Cohen Oracle c.c.c. J. Appl. Anal. Submitted, math.LO/0303294
Shelah, S.: On nicely definable forcing notions. J. Appl. Anal. Accepted, math.LO/0303293
Shelah, S.: On what I do not understand (and have something to say). Fundamenta Math. 166, 1–82 (2000) math.LO/9906113
Shelah, S.: On what I do not understand (and have something to say), model theory. Math. Japonica 51, 329–377 (2000) math.LO/9910158
Shelah, S.: Can you take Solovay’s inaccessible away? Israel J. Math. 48, 1–47 (1984)
Shelah, S.: How special are Cohen and random forcings i.e. Boolean algebras of the family of subsets of reals modulo meagre or null. Israel J. Math. 88, 159–174 (1994) math.LO/9303208
Shelah, S.: Classification theory and the number of nonisomorphic models. volume 92 of Studies in Logic and the Foundations of Math. North-Holland Publishing Co., Amsterdam, 1990, pp. xxxiv+705
Shelah, S.: Proper and improper forcing. Perspectives in Math. Logic. Springer, 1998
Solecki, S.: Analytic ideals and their applications. Ann. Pure Appl. Logic 99, 51–72 (1999)
Solovay, R.M.: A model of set theory in which every set of reals is Lebesgue measurable. Ann. Math. 92, 1–56 (1970)
Solovay, R.M., Tennenbaum, S.: Iterated Cohen extensions and Souslin’s problem. Ann. Math. 94, 201–245 (1971)
Stern, J.: Regularity properties of definable sets of reals. Ann. Pure Appl. Logic 29, 289–324 (1985)
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The first author thanks the Hebrew University of Jerusalem for its hospitality during his visits to Jerusalem. His research was also partially supported by a grant from the University Committee on Research of UNO
The research of the second author was partially supported by the Israel Science Foundation. Publication 672
Mathematics Subject Classification (2000): Primary 03E35 Secondary; 03E40, 03E05
Revised version: 30 September 2003
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Rosłanowski, A., Shelah, S. Sweet & sour and other flavours of ccc forcing notions. Arch. Math. Logic 43, 583–663 (2004). https://doi.org/10.1007/s00153-004-0213-7
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DOI: https://doi.org/10.1007/s00153-004-0213-7