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The recursively enumerable degrees
- in Handbook of Computability Theory, Studies in Logic and the Foundations of Mathematics 140
, 1996
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Prospects for mathematical logic in the twenty-first century
- BULLETIN OF SYMBOLIC LOGIC
, 2002
"... The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently. ..."
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Cited by 6 (0 self)
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The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.
A Splitting Theorem for n-REA Degrees
"... We prove that, for any D, A and U with D > T A # U and r.e. in A# U , there are pairs X 0 , X 1 and Y 0 , Y 1 such that D # T X 0 #X 1 ; D # T Y 0 # Y 1 ; and, for any i and j from {0, 1} and any set B, if X i #A # T B and Y j # A # T B then A # T B. We then deduce that for any degrees d, a, and b s ..."
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Cited by 5 (5 self)
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We prove that, for any D, A and U with D > T A # U and r.e. in A# U , there are pairs X 0 , X 1 and Y 0 , Y 1 such that D # T X 0 #X 1 ; D # T Y 0 # Y 1 ; and, for any i and j from {0, 1} and any set B, if X i #A # T B and Y j # A # T B then A # T B. We then deduce that for any degrees d, a, and b such that a and b are recursive in d, a ## T b, and d is n-REA in to a, d can be split over a avoiding b. This shows that the Main Theorem of Cooper [1990] and [1993] is false.
Conjectures and Questions from Gerald Sacks’s Degrees of Unsolvability
- Archive for Mathematical Logic
, 1993
"... We describe the important role that the conjectures and questions posed at the end of the two editions of Gerald Sacks's Degrees of Unsolvability have had in the development of recursion theory over the past thirty years. Gerald Sacks has had a major influence on the development of logic, particular ..."
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Cited by 3 (1 self)
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We describe the important role that the conjectures and questions posed at the end of the two editions of Gerald Sacks's Degrees of Unsolvability have had in the development of recursion theory over the past thirty years. Gerald Sacks has had a major influence on the development of logic, particularly recursion theory, over the past thirty years through his research, writing and teaching. Here, I would like to concentrate on just one instance of that influence that I feel has been of special significance to the study of the degrees of unsolvability in general and on my own work in particular--- the conjectures and questions posed at the end of the two editions of Sacks's first book, the classic monograph Degrees of Unsolvability (Annals
