Abstract
We prove thatMA(σ-centered) + the Dual Borel Conjecture is consistent; and thatMA(σ-centered) + the non-additivity of the ideal of the strong measure zero sets also is consistent.
Similar content being viewed by others
References
M. Bell,On the combinatorial principle P(c), Fund. Math.134 (1989), 147–149.
T. Bartoszynski,Additivity of measure implies additivity of category, Trans. Am. Math. Soc.281 (1984), 209–213.
T. Carlson, unpublished notes.
J. Ihoda,Strong measure zero set and rapid filters, J. Symb. Logic53 (1988).
J. Ihoda and S. Shelah,Souslin forming, J. Symb. Logic53 (1988).
K. Kunen,Set Theory, North-Holland, Amsterdam, 1980.
G. G. Lorentz,On a problem of additive number theory, Proc. Am. Math. Soc.,5 (1954).
D. Martin and R. Solovay,Internal Cohen extensions, Ann. Math. Logic, to appear.
J. Pawlikowski,Powers of transitive bases of measure and category, Proc. Am. Math. Soc.93 (1985), 719–729.
J. Roitman,Adding a random or a Cohen real: topological consequences and the effect on Martin’s axiom, Fund. Math.C111 (1979), 47–60.
S. Shelah,Can you take Solovay’s inaccessible away? Isr. J. Math.48 (1984), 1–47.
Author information
Authors and Affiliations
Additional information
Jaime Ihoda.
Rights and permissions
About this article
Cite this article
Judah, H., Shelah, S. MA(σ-centered): Cohen reals, strong measure zero sets and strongly meager sets. Israel J. Math. 68, 1–17 (1989). https://doi.org/10.1007/BF02764965
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02764965