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The nonexistence of robust codes for subsets of ω₁

100%

Asperó D.

Fundamenta Mathematicae

2005

tom 186

nr 3

215-231

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).

On simple partitions of $[κ]^{κ}$

100%

Asperó D.

Fundamenta Mathematicae

2003

tom 177

nr 2

139-149

For every uncountable regular cardinal κ, every κ-Borel partition of the space of all members of $[κ]^{κ}$ whose enumerating function does not have fixed points has a homogeneous club.

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2 Fundamenta Mathematicae

2 Asperó D.

1 2005

1 2003

Wyniki wyszukiwania

The nonexistence of robust codes for subsets of ω₁

On simple partitions of $[κ]^{κ}$