# Computability Theory and Its Applications: Current Trends and Open Problems

### About this Title

**Peter A. Cholak**, **Steffen Lempp**, **Manuel Lerman** and **Richard A. Shore**, Editors

Publication: Contemporary Mathematics

Publication Year
2000: Volume 257

ISBNs: 978-0-8218-1922-7 (print); 978-0-8218-7847-7 (online)

DOI: http://dx.doi.org/10.1090/conm/257

MathSciNet review: 1770798

### Table of Contents

**Front/Back Matter**

**Articles**

- Klaus Ambos-Spies and Antonín Kučera – Randomness in computability theory [MR 1770730]
- Marat Arslanov – Open questions about the $n$-c.e. degrees [MR 1770731]
- Serikzhan Badaev and Sergey Goncharov – The theory of numberings: open problems [MR 1770732]
- Douglas Cenzer and Carl G. Jockusch, Jr. – $\Pi _1^0$ classes—structure and applications [MR 1770733]
- Peter A. Cholak – The global structure of computably enumerable sets [MR 1770734]
- C. T. Chong and Yue Yang – Computability theory in arithmetic: provability, structure and techniques [MR 1770735]
- Randall Dougherty and Alexander S. Kechris – How many Turing degrees are there? [MR 1770736]
- Rod Downey and J. B. Remmel – Questions in computable algebra and combinatorics [MR 1770737]
- Harvey Friedman and Stephen G. Simpson – Issues and problems in reverse mathematics [MR 1770738]
- Sergey Goncharov and Bakhadyr Khoussainov – Open problems in the theory of constructive algebraic systems [MR 1770739]
- Marcia Groszek – Independence results from ZFC in computability theory: some open problems [MR 1770740]
- Julia F. Knight – Problems related to arithmetic [MR 1770741]
- Manuel Lerman – Embeddings into the computably enumerable degrees [MR 1770742]
- André Nies – Definability in the c.e. degrees: questions and results [MR 1770743]
- Piergiorgio Odifreddi – Strong reducibilities, again [MR 1770744]
- Mikhail Peretyat′kin – Finitely axiomatizable theories and Lindenbaum algebras of semantic classes [MR 1770745]
- Alexandra Shlapentokh – Towards an analog of Hilbert’s tenth problem for a number field [MR 1770746]
- Richard A. Shore – Natural definability in degree structures [MR 1770747]
- Theodore A. Slaman – Recursion theory in set theory [MR 1770748]
- Robert I. Soare – Extensions, automorphisms, and definability [MR 1770749]
- Andrea Sorbi – Open problems in the enumeration degrees [MR 1770750]