Add to ORKGIf x0 and x1 are both generic, the theories of the degrees below x0 and x1 are the same. The same is true if both are random. We show that the n-genericity or n-randomness of x do not su¢ce to guarantee that the degrees below x have these common theories. We also show that these two theories (for generics and randoms) are di¤erent. These results answer questions of Jockusch as well as Barmpalias, Day and Lewis.
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
We prove a number of results in effective randomness, using methods in which π⁰₁ classes play an ess...
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
Abstract. We say that A ≤LR B if every B-random number isA-random. Intuitively this means that if or...
A set A is a basis for Schnorr randomness if and only if it is Turing reducible to a set R which is ...
We say that A≤LRB if every B-random number is A-random. Intuitively this means that if oracle A can ...
We say that A≤LRB if every B-random number is A-random. Intuitively this means that if oracle A can ...
We investigate the truth-table degrees of (co-)c.e.\ sets, in particular,sets of random strings. It ...
This thesis establishes results in several different areas of computability theory. The first chapt...
We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study ...
We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study ...
Abstract. We compare various notions of algorithmic randomness. First we consider relativized random...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
We prove a number of results in effective randomness, using methods in which π⁰₁ classes play an ess...
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
Abstract. We say that A ≤LR B if every B-random number isA-random. Intuitively this means that if or...
A set A is a basis for Schnorr randomness if and only if it is Turing reducible to a set R which is ...
We say that A≤LRB if every B-random number is A-random. Intuitively this means that if oracle A can ...
We say that A≤LRB if every B-random number is A-random. Intuitively this means that if oracle A can ...
We investigate the truth-table degrees of (co-)c.e.\ sets, in particular,sets of random strings. It ...
This thesis establishes results in several different areas of computability theory. The first chapt...
We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study ...
We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study ...
Abstract. We compare various notions of algorithmic randomness. First we consider relativized random...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
Abstract. We prove a number of results in effective randomness, using methods in which Π01 classes p...
We prove a number of results in effective randomness, using methods in which π⁰₁ classes play an ess...