Special subsets of the reals and tree forcing notions
HTML articles powered by AMS MathViewer
- by Marcin Kysiak, Andrzej Nowik and Tomasz Weiss PDF
- Proc. Amer. Math. Soc. 135 (2007), 2975-2982 Request permission
Abstract:
We study relationships between classes of special subsets of the reals (e.g. meager-additive sets, $\gamma$-sets, $C''$-sets, $\lambda$-sets) and the ideals related to the forcing notions of Laver, Mathias, Miller and Silver.References
- Tomek Bartoszyński and Haim Judah, Set theory, A K Peters, Ltd., Wellesley, MA, 1995. On the structure of the real line. MR 1350295, DOI 10.1201/9781439863466
- Jörg Brendle and Benedikt Löwe, Solovay-type characterizations for forcing-algebras, J. Symbolic Logic 64 (1999), no. 3, 1307–1323. MR 1779764, DOI 10.2307/2586632
- Jack B. Brown, The Ramsey sets and related sigma algebras and ideals, Fund. Math. 136 (1990), no. 3, 179–185. MR 1095690, DOI 10.4064/fm-136-3-179-185
- Lorenz Halbeisen, Making doughnuts of Cohen reals, MLQ Math. Log. Q. 49 (2003), no. 2, 173–178. MR 1961459, DOI 10.1002/malq.200310016
- Marcin Kysiak and Tomasz Weiss, Small subsets of the reals and tree forcing notions, Proc. Amer. Math. Soc. 132 (2004), no. 1, 251–259. MR 2021269, DOI 10.1090/S0002-9939-03-07026-6
- A. W. Miller, Handbook of set-theoretic topology, ch. Special Subsets of the Real Line, pp. 201–233, North-Holland, Amsterdam, 1984.
- Arnold W. Miller, Special sets of reals, Set theory of the reals (Ramat Gan, 1991) Israel Math. Conf. Proc., vol. 6, Bar-Ilan Univ., Ramat Gan, 1993, pp. 415–431. MR 1234286
- —, A hodgepodge of sets of reals, Preprint (2006).
- Andrej Nowik, Marion Scheepers, and Tomasz Weiss, The algebraic sum of sets of real numbers with strong measure zero sets, J. Symbolic Logic 63 (1998), no. 1, 301–324. MR 1610427, DOI 10.2307/2586602
- Andrzej Nowik and Tomasz Weiss, On the Ramseyan properties of some special subsets of $2^\omega$ and their algebraic sums, J. Symbolic Logic 67 (2002), no. 2, 547–556. MR 1905154, DOI 10.2178/jsl/1190150097
- Andrzej Nowik and Tomasz Weiss, Strongly meager sets of real numbers and tree forcing notions, Proc. Amer. Math. Soc. 130 (2002), no. 4, 1183–1187. MR 1873795, DOI 10.1090/S0002-9939-01-06174-3
- John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443, DOI 10.1007/978-1-4684-9339-9
Additional Information
- Marcin Kysiak
- Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland
- Email: mkysiak@mimuw.edu.pl
- Andrzej Nowik
- Affiliation: Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
- Email: nowik@math.uni.gda.pl
- Tomasz Weiss
- Affiliation: Institute of Mathematics and Physics, Akademia Podlaska, ul. 3-go Maja, 08-110 Siedlce, Poland
- MR Author ID: 631175
- ORCID: 0000-0001-9201-7202
- Email: tomaszweiss@o2.pl
- Received by editor(s): March 13, 2006
- Received by editor(s) in revised form: June 8, 2006
- Published electronically: May 9, 2007
- Additional Notes: A part of the research was made when the first author was visiting the Institute of Mathematics of the Polish Academy of Sciences
The second author was partially supported by grant BW/5100-5-0201-6 - Communicated by: Julia Knight
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2975-2982
- MSC (2000): Primary 03E05, 03E35, 28E15, 54G99
- DOI: https://doi.org/10.1090/S0002-9939-07-08808-9
- MathSciNet review: 2317976