Includes bibliographical references.

Randomness in computability theory ; Open questions about the .e. degrees ; The theory of numberings: open problems ; Pi _1^0 classes structure and applications ; The global structure of computably enumerable sets ; Computability theory in arithmetic: provability, structure and techniques ; How many Turing degrees are there? ; Questions in computable algebra and combinatorics ; Issues and problems in reverse mathematics ; Open problems in the theory of constructive algebraic systems ; Independence results from ZFC in computability theory: some open problems ; Problems related to arithmetic ; Embeddings into the computably enumerable degrees ; Definability in the c.e. degrees: questions and results ; Strong reducibilities, again ; Finitely axiomatizable theories and Lindenbaum algebras of semantic classes ; Towards an analog of Hilbert's tenth problem for a number field ; Natural definability in degree structures ; Recursion theory in set theory ; Extensions, automorphisms, and definability ; Open problems in the enumeration degrees Klaus AmbosSpies and Antonin Kucera ; Marat Arslanov ; Serikzhan Badaev and Sergey Goncharov ; Douglas Cenzer and Carl G Jockusch Jr ; Peter A Cholak ; C T Chong and Yue Yang ; Randall Dougherty and Alexander S Kechris ; Rod Downey and J B Remmel ; Harvey Friedman and Stephen G Simpson ; Sergey Goncharov and Bakhadyr Khoussainov ; Marcia Groszek ; Julia F Knight ; Manuel Lerman ; Andre Nies ; Piergiorgio Odifreddi ; Mikhail Peretyatkin ; Alexandra Shlapentokh ; Richard A Shore ; Theodore A Slaman ; Robert I Soare ; Andrea Sorbi