We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions ofO(1)-deepK,O(1)-deepC, order-deepKand order-deepCsequences. Our main results are that Martin-L ̈of randomsets are not order-deepC, that every many-one degree contains a set which is notO(1)-deepC, thatO(1)-deepCsetsand order-deepKsets have high or DNR Turing degree and that noK-trival set isO(1)-deepK
SETS, MODELS, AND PROOFS: TOPICS IN THE THEORY OF RECURSIVE FUNCTIONS David Roger Belanger, Ph.D. Co...
Abstract. An n-r.e. set can be defined as the symmetric difference of n recursively enumerable sets....
In Recursion Theory (Computability Theory), we study Turing degrees in terms of their degree-theoret...
We study Bennett deep sequences in the context of recursion theory; in particular we investigate the...
A sequence is Bennett deep [5] if every recursive approximation of the Kolmogorov complexity of its...
We introduce the notion of limit-depth, as a notion similar to Bennett depth, but well behaved on T...
We show there is a non-recursive r.e. set A such that if W is any low r.e. set, then the join W # ...
AbstractIn the 1980s, Bennett introduced computational depth as a formal measure of the amount of co...
this paper. Clearly the most remarkable result relating the jump operator to the ordering of degrees...
We introduce a general framework for defining the depth of an infinite binary sequence with respect...
This paper investigates Bennett\u27s notions of strong and weak computational depth (also called log...
AbstractThis paper reviews and investigates Bennett's notions of strong and weak computational depth...
We study the degrees below 0$\sp\prime$ by examining some phenomena relating two well-known hierarch...
. An infinite binary sequence x is defined to be 1. strongly useful if there is a recursive time bou...
We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study ...
SETS, MODELS, AND PROOFS: TOPICS IN THE THEORY OF RECURSIVE FUNCTIONS David Roger Belanger, Ph.D. Co...
Abstract. An n-r.e. set can be defined as the symmetric difference of n recursively enumerable sets....
In Recursion Theory (Computability Theory), we study Turing degrees in terms of their degree-theoret...
We study Bennett deep sequences in the context of recursion theory; in particular we investigate the...
A sequence is Bennett deep [5] if every recursive approximation of the Kolmogorov complexity of its...
We introduce the notion of limit-depth, as a notion similar to Bennett depth, but well behaved on T...
We show there is a non-recursive r.e. set A such that if W is any low r.e. set, then the join W # ...
AbstractIn the 1980s, Bennett introduced computational depth as a formal measure of the amount of co...
this paper. Clearly the most remarkable result relating the jump operator to the ordering of degrees...
We introduce a general framework for defining the depth of an infinite binary sequence with respect...
This paper investigates Bennett\u27s notions of strong and weak computational depth (also called log...
AbstractThis paper reviews and investigates Bennett's notions of strong and weak computational depth...
We study the degrees below 0$\sp\prime$ by examining some phenomena relating two well-known hierarch...
. An infinite binary sequence x is defined to be 1. strongly useful if there is a recursive time bou...
We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study ...
SETS, MODELS, AND PROOFS: TOPICS IN THE THEORY OF RECURSIVE FUNCTIONS David Roger Belanger, Ph.D. Co...
Abstract. An n-r.e. set can be defined as the symmetric difference of n recursively enumerable sets....
In Recursion Theory (Computability Theory), we study Turing degrees in terms of their degree-theoret...
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