Abstract
Abstract
We investigate the notion of strong measure zero sets in the context of the higher Cantor space
$2^\kappa $
for
$\kappa $
at least inaccessible. Using an iteration of perfect tree forcings, we give two proofs of the relative consistency of
$$\begin{align*}|2^\kappa| = \kappa^{++} + \forall X \subseteq 2^\kappa:\ X \textrm{ is strong measure zero if and only if } |X| \leq \kappa^+. \end{align*}$$
Furthermore, we also investigate the stronger notion of stationary strong measure zero and show that the equivalence of the two notions is undecidable in ZFC.
Publisher
Cambridge University Press (CUP)
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