Structure and Randomness in Computability and Set Theory

Structure and Randomness in Computability and Set TheoryThis volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF supported annual Southeastern Logic

This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium.

Contents: Limits of the Kucerea-Gacs Coding Method (George Barmpalias and Andrew Lewis-Pye); Infinitary partition properties of sums of selective ultrafilters (Andreas Blass); Semiselective Coideals and Ramsey Sets (Carlos DiPrisco and Leonardo Pacheco); Survey on Topological Ramsey Spaces Dense in Forcings (Natasha Dobrinen); Higher Computability in the Reverse Mathematics of Borel Determinacy (Sherwood Hachtman); Computability and Definability (Valentina Harizanov); A Ramsey Space of Infinite Polyhedra and the Random Polyhedron (Jose G Mijares Palacios and Gabriel Padilla); Computable Reducibility for Cantor Space (Russell G Miller); Information vs Dimension - An Algorithmic Perspective (Jan Reimann);

Readership: Graduate students and researchers interested in the interface between set theory and computability.