On nicely definable forcing notions

• Autorzy: Shelah S.
• Języki publikacji: EN

Abstrakty

EN

We prove that if Q is a new-nep forcing then it cannot add a dominating real. We also show that amoeba forcing cannot be P(X) / I if I is an N1-complete ideal. Furthermore, we generalize the results of [12].

Słowa kluczowe

EN

set theory forcing; set theory of the reals; nep forcing

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2005
• Tom: Vol. 11, nr 1
• Strony: 1--17
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Shelah S.

• The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel
• Department of Mathematics, Hill Center — Busch Campus, Rutgers, The State University of New Jersey, L10 Frelinghuysen Road Piscataway, NJ 08854-8019 USA

Bibliografia

• [1] Bartoszyński, T., Rosłanowski, A., Towards Martin's minimum,, Arch. Math. Logic, 41 (2002), 65-82. math.L0/9904163./.
• [2] Brendle, J., Combinatorial properties of classical forcing notions, Ann. Pure Appl. Logic, 73 (1995), 143-170.
• [3] Brendle, J., Judah, H., Shelah, S., Combinatorial properties of Hechler forcing. Ann. Pure Appl. Logic, 58 (1992), 185-199. math.LO/9211202.
• [4] Gitik, M., Shelah, S., Forcings with ideals and simple forcing notions, Israel J. Math., 68 (1989), 129-160.
• [5] Gitik, M., Shelah, S., More on simple forcing notions and forcings with ideals, Ann. Pure Appl. Logic, 59 (1993), 219-238.
• [6] Gitik, M., Shelah, S., More on real-valued measurable cardinals and forcing with ideals, Israel J. Mathematics, 124 (2001), 221-242. math.LO/9507208.
• [7] Goldstern, M., Judah, H., Iteration of Souslin forcing, projective measurability and the Borel conjecture. Israel J. Math. 78 (1992), 335-362.
• [8] Ihoda, J. (Judah Haim), Shelah, S., Souslin forcing, J. Symbolic Logic 53 (1988), 1188-1207.
• [9] Keisler, J. 14., Model Theory for Infinitary Logic. Logic with Countable Conjunctions and Finite Quantifiers, Stud. Logic Pound. Math. 62, North-Holland Publishing Co., Amsterdam-London, 1971.
• [10] Rosłanowski, A., Shelah, S., Sweet & sour and other flavours of ccc forcing notions. Arch. Math. Logic 43 (2004). 583-663. math.LO/9909115.
• [11] Rosłanowski, A., Shelah, S., Norms on Possibilities I: Forcing with Trees and Creatures, Mem. Amer. Math. Soc, 141(671), Providence, RI, 1999. math.LO/9807172.
• [12] Shelah, S., How special arc Cohen and random forcings i.e. Boolean algebras of the family of subsets of reals modulo meagre or null, Israel J. Math., 88 (1994), 159-174. math. L079303208.
• [13] Shelah, S., On what I do not understand (and have something to say): Part I. Fund. Math. 166 (2000), 1-82. math.LO/9906113.
• [14] Shelah, S., Properties» without elementaricity. J. Appl. Anal. 10(2) (2004), 169-289. math.L0/9712283.
• [15] Shelah, S., More on nw-nep forcing notions.