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H. Rogers (1958)
Gödel numberings of partial recursive functionsJournal of Symbolic Logic, 23
R. Soare (1987)
Recursively enumerable sets and degreesBulletin of the American Mathematical Society, 84
D. Cenzer, J. Remmel (1999)
Handbook of Recursive Mathematics
S. Binns (2006)
Small $${\Pi^{0}_{1}}$$ classesArch. Math. Logic, 45
S. Goncharov, S. Lempp, D. Solomon (2002)
Friedberg Numberings of Families of n-Computably Enumerable SetsAlgebra and Logic, 41
(2007)
Enumerations of Π 0 1 classes: acceptability and decidable classes, Elect. Notes in Th
C. Jockusch, R. Soare (1972)
$${\Pi^{0}_{1}}$$ classes and degrees of theoriesTrans. Am. Math. Soc., 173
R. Downey (1987)
Maximal theoriesAnn. Pure App. Logic, 33
S. Binns (2006)
Small Π01 ClassesArchive for Mathematical Logic, 45
Effectively Closed Sets, ASL Lecture Notes in Logic
Brodhead. Effectively Closed Sets and Enumerations. Submitted
P. Hinman (1978)
Recursion-Theoretic Hierarchies
R. Downey, C. Jockusch, M. Stob (1990)
Recursion Theory Week: Proc. Ober. 1989
D. Cenzer, R. Downey, C. Jockusch, R. Shore (1993)
Countable Thin Pi01 ClassesAnn. Pure Appl. Log., 59
P. Odifreddi (1989)
Classical recursion theory
Rod Downey, D. Hirschfeldt (2010)
Algorithmic Randomness and Complexity
R. Downey, C. Jockusch, M. Stob (1990)
Array nonrecursive sets and multiple permitting arguments
P. Cholak, R. Coles, R. Downey, E. Hermann (2001)
Automorphisms of the lattice of $${\Pi^{0}_{1}}$$ classes: perfect thin classes and anc degreesTrans. Am. Math. Soc., 353
(1972)
Amer. Math. Soc
(2003)
ANNALS OF PURE AND APPLIED LOGIC
Z. Adamowicz (1991)
On maximal theoriesJournal of Symbolic Logic, 56
S. Lempp (1987)
Hyperarithmetical index sets in recursion theoryTransactions of the American Mathematical Society, 303
D. Cenzer, J. Remmel (1998)
Index sets for $${\Pi^{0}_{1}}$$ classesAnn. Pure App. Logic, 93
Y. Ershov (1999)
Theory of Numberings
Thin classes of separating sets
A. Raichev (2006)
RELATIVE RANDOMNESS VIA RK-REDUCIBILITY
R. Goodstein, H. Rogers (1969)
Theory of Recursive Functions and Effective ComputabilityThe Mathematical Gazette, 53
Paul Brodhead (2008)
Computable aspects of closed sets
Yoshindo Suzuki (1959)
Enumeration of Recursive SetsJournal of Symbolic Logic, 24
D. Cenzer, J. Remmel (1998)
Index Sets for Pi01 ClassesAnn. Pure Appl. Log., 93
(2006)
Elect. Notes in Th. Comp. Sci
(1999)
Π 0 1 classes in mathematics, in: Handbook of recursive mathematics
Peter Cholak, R. Coles, R. Downey, E. Herrmann (2001)
Automorphisms of the lattice of Π₁⁰ classes; perfect thin classes and anc degreesTransactions of the American Mathematical Society, 353
C. Jockusch, R. Soare (1972)
Π⁰₁ classes and degrees of theoriesTransactions of the American Mathematical Society, 173
Jr. Rogers (1969)
Theory of Recursive Functions and Effective Computability
E. Griffor (1999)
Handbook of Computability Theory, 140
(1999)
Index sets for computable real functions, Theor
R. Friedberg (1958)
Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplicationJournal of Symbolic Logic, 23
R. Friedberg (1958)
Three theorems on recursive enumerationJ. Symb. Logic, 23
M. Pour-El, H. Putnam (1965)
Recursively enumerable classes and their application to recursive sequences of formal theoriesArchiv für mathematische Logik und Grundlagenforschung, 8
Enum. of Π 0 1 Cl.: Accep. and Dec. Cl
S. Simpson (2005)
Mass Problems and RandomnessBulletin of Symbolic Logic, 11
D. Cenzer, R. Downey, C. Jockusch, R. Shore (1993)
Countable thin $${\Pi^{0}_{1}}$$ classesAnn. Pure App. Logic, 59
An effectively closed set, or $${\Pi^{0}_{1}}$$ class, may viewed as the set of infinite paths through a computable tree. A numbering, or enumeration, is a map from ω onto a countable collection of objects. One numbering is reducible to another if equality holds after the second is composed with a computable function. Many commonly used numberings of $${\Pi^{0}_{1}}$$ classes are shown to be mutually reducible via a computable permutation. Computable injective numberings are given for the family of $${\Pi^{0}_{1}}$$ classes and for the subclasses of decidable and of homogeneous $${\Pi^{0}_{1}}$$ classes. However no computable numberings exist for small or thin classes. No computable numbering of trees exists that includes all computable trees without dead ends.
Archive for Mathematical Logic – Springer Journals
Published: Apr 12, 2008
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