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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/1908.10718 |
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- We investigate the notion of strong measure zero sets in the context of the higher Cantor space $2^κ$ for $κ$ at least inaccessible. Using an iteration of perfect tree forcings, we give two proofs of the relative consistency of \[ |2^κ| = κ^{++} + \forall X \subseteq 2^κ:\ X \text{ is strong measure zero if and only if } |X| \leq κ^+. \] 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.