The nonexistence of robust codes for subsets of ω₁

• Autorzy: David Asperó
• Języki publikacji: EN

Abstrakty

EN

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 $⟨S_α: α < ω₁⟩$ of pairwise disjoint stationary subsets of ω₁, where "robustness" of r as a code may either mean that $S ∈ L[r,⟨S*_α: α < ω₁⟩]$ whenever each $S*_α$ is equal to $S_α$ modulo nonstationary changes, or may have the weaker meaning that $S ∈ L[r,⟨S_α ∩ C: α < ω₁⟩]$ for every club C ⊆ ω₁. 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 ω₁ into ω₁).

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 03E55: Large cardinals
• 03E20: Other classical set theory (including functions, relations, and set algebra)
• 03E45: Inner models, including constructibility, ordinal definability, and core models
• 03E47: Other notions of set-theoretic definability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 186
• Numer: 3
• Strony: 215-231

Daty

wydano

2005

Twórcy

autor

David Asperó

• Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, England, UK

Identyfikatory

DOI

10.4064/fm186-3-2