The nonexistence of robust codes for subsets of ω

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Abstract

Several results are presented concerning the existence or nonexistence, for a subset S of ? , of a real r which works as a robust code for S with respect to a given sequence of pairwise disjoint stationary subsets of ? , where "robustness" of r as a code may either mean that S ? L[r, ] whenever each S * is equal to S modulo nonstationary changes, or may have the weaker meaning that S ? L[r, ] for every club C ? ? . Variants of the above theme are also considered which result when the requirement that S gets exactly coded is replaced by the weaker requirement that some set is coded which is equal to S up to a club, and when sequences of stationary sets are replaced by decoding devices possibly carrying more information (like functions from ? into ? ).
Original languageEnglish
Pages (from-to)215-231
Number of pages17
JournalFundamenta Mathematicae
Volume186
Issue number3
Publication statusPublished - 1 Jan 2005

Keywords

  • ℙ max extensions of L(ℝ)
  • Forcing axioms
  • Robust codes for subsets of ω 1
  • Sequences of stationary subsets of ω 1

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