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The nonexistence of robust codes for subsets of ω₁

David Asperó (2005)

Fundamenta Mathematicae

Several results are presented concerning the existence or nonexistence, for a subset S of ω₁, of a real r which works as a robust code for S with respect to a given sequence S α : α < ω of pairwise disjoint stationary subsets of ω₁, where “robustness” of r as a code may either mean that S L [ r , S * α : α < ω ] whenever each S * α is equal to S α modulo nonstationary changes, or may have the weaker meaning that S L [ r , S α C : α < ω ] for every club C ⊆ ω₁. Variants of the above theme are also considered which result when the requirement that S gets exactly...

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