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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.
Preface
v
About the Editors
xvii
Part I Infinitary Combinatorics and Ultrafilters
1
(84)
1 Topological Ramsey Spaces Dense in Forcings
3
(56)
Natasha Dobrinen
2 Infinitary Partition Properties of Sums of Selective Ultrafilters
59
(26)
Andreas Blass
Part II Algorithmic Randomness and Information
85
(68)
3 Limits of the Kucera--Gacs Coding Method
87
(24)
George Barmpalias
Andrew Lewis-Pye
4 Information vs. Dimension: An Algorithmic Perspective