The nonexistence of robust codes for subsets of ω₁

David Asperó. "The nonexistence of robust codes for subsets of ω₁." Fundamenta Mathematicae 186.3 (2005): 215-231. <http://eudml.org/doc/282931>.

@article{DavidAsperó2005,
abstract = {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).},
author = {David Asperó},
journal = {Fundamenta Mathematicae},
keywords = {robust codes for subsets of ; sequences of stationary subsets of ; forcing axioms; extensions of },
language = {eng},
number = {3},
pages = {215-231},
title = {The nonexistence of robust codes for subsets of ω₁},
url = {http://eudml.org/doc/282931},
volume = {186},
year = {2005},
}

TY - JOUR
AU - David Asperó
TI - The nonexistence of robust codes for subsets of ω₁
JO - Fundamenta Mathematicae
PY - 2005
VL - 186
IS - 3
SP - 215
EP - 231
AB - 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).
LA - eng
KW - robust codes for subsets of ; sequences of stationary subsets of ; forcing axioms; extensions of 
UR - http://eudml.org/doc/282931
ER -