Priority arguments using iterated trees of strategies

A general framework for priority arguments in classical recursion theory, using iterated trees of strategies, is introduced and used to present new proofs of four fundamental theorems of recursion theory.

[1]  R. Shore.  The recursively enumerable α-degrees are dense , 1976 .

[2]  A. H. Lachlan.  The priority method for the construction of recursively enumerable sets , 1973 .

[3]  A. Lachlan.  On Some Games Which Are Relevant to the Theory of Recursively Enumerable Sets , 1970 .

[4]  Richard A. Shore,et al.  A non-inversion theorem for the jump operator , 1988, Ann. Pure Appl. Log..

[5]  A. R. D. Mathias,et al.  Cambridge Summer School in Mathematical Logic , 1973 .

[6]  Gerald E. Sacks,et al.  Recursive enumerability and the jump operator , 1963 .

[7]  Robert I. Soare,et al.  The infinite injury priority method , 1976, Journal of Symbolic Logic.

[8]  R. Friedberg,et al.  TWO RECURSIVELY ENUMERABLE SETS OF INCOMPARABLE DEGREES OF UNSOLVABILITY (SOLUTION OF POST'S PROBLEM, 1944). , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Antonín Kučera.  On the use of Diagonally Nonrecursive Functions , 1989 .

[10]  Christopher J. Ash,et al.  Labelling Systems and r.e. Structures , 1990, Ann. Pure Appl. Log..

[11]  Antonín Kucera,et al.  An Alternative, Priority-Free, Solution to Post's Problem , 1996, MFCS.

[12]  Christopher J. Ash.  Stability of recursive structures in arithmetical degrees , 1986, Ann. Pure Appl. Log..

[13]  Manuel Lerman.  Admissible ordinals and priority arguments , 1973 .

[14]  G. Sacks.  ON THE DEGREES LESS THAN 0 , 1963 .

[15]  R. Soare.  Recursively enumerable sets and degrees , 1987 .