Sacks forcing, Laver forcing, and Martin's axiom

DOI10.1007/BF01269943zbMath0755.03026WikidataQ114693987 ScholiaQ114693987MaRDI QIDQ1190614

Saharon Shelah, Haim Judah, Arnold W. Miller

Publication date: 26 September 1992

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

zbMATH Keywords

additivityMartin's axiomSacks forcingLaver forcingcardinals associated with Marczewski's ideal \(s^ 0\)

Mathematics Subject Classification ID

Consistency and independence results (03E35) Continuum hypothesis and Martin's axiom (03E50) Other aspects of forcing and Boolean-valued models (03E40)

Related Items (26)

Silver trees and Cohen reals ⋮ Combinatorial properties of classical forcing notions ⋮ The covering number of the strong measure zero ideal can be above almost everything else ⋮ No Tukey reduction of Lebesgue null to Silver null sets ⋮ Strongly dominating sets of reals ⋮ Generic constructions of small sets of reals ⋮ Strongly unbounded and strongly dominating sets of reals generalized ⋮ Ramsey sets, the Ramsey ideal, and other classes overR ⋮ Cardinal invariants and the collapse of the continuum by Sacks forcing ⋮ Generic trees ⋮ Different cofinalities of tree ideals ⋮ Universal sets for ideals ⋮ Families of sets with nonmeasurable unions with respect to ideals defined by trees ⋮ Distinguishing types of gaps in (ω)/fin ⋮ Definable Hamel bases and ${\sf AC}_\omega ({\mathbb R})$ ⋮ A Sacks amoeba preserving distributivity of $\mathcal {P}(\omega )/\mathrm {fin}$ ⋮ Happy families and completely Ramsey sets ⋮ On Tree Ideals ⋮ Towers on Trees ⋮ Additivity of the two-dimensional Miller ideal ⋮ On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology ⋮ Borel Conjecture, dual Borel Conjecture, and other variants of the Borel Conjecture ⋮ NONMEASURABLE SETS AND UNIONS WITH RESPECT TO TREE IDEALS ⋮ Tukey reductions of nowhere Ramsey to Silver null sets ⋮ Antichains of perfect and splitting trees ⋮ SILVER ANTICHAINS

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