1993•Journal of Symbolic LogicRequires access

Strong measure zero sets without Cohen reals

Martin Goldstern, Haim Judah, Saharon Shelah

Abstract

Abstract If ZFC is consistent, then each of the following is consistent with : (1) X ⊆ ℝ is of strong measure zero iff ∣X∣ ≤ ℵ1 + there is a generalized Sierpinski set. (2) The union of ℵ many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size ℵ2 + there is no Cohen real over L.

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Key concepts: Zero (linguistics), Measure (data warehouse), Null set, Mathematics, Set (abstract data type), Zero set, Combinatorics, Discrete mathematics