Add to ORKGAbstract. We prove a number of results in effective randomness, using methods in which Π01 classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem. §1. Introduction. 1.1. Π01 classes in computability and effective randomness. Many arguments in computability theory and algorithmic randomness involve Π01 sets of reals and techniques specific to such sets in an essential way. Two major references to such arguments in computability theory and in particular the degrees of unsolvability
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
Abstract. A relatively longstanding question in algorithmic randomness is Jan Reimann’s question whe...
The set A is low for Martin-Lof random if each random set is already random relative to A. A is K-t...
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...
Abstract. We say that A ≤LR B if every B-random number isA-random. Intuitively this means that if or...
Abstract. We compare various notions of algorithmic randomness. First we consider relativized random...
We say that A≤LRB if every B-random number is A-random. Intuitively this means that if oracle A can ...
Abstract. Every K-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Marti...
This thesis establishes results in several different areas of computability theory. The first chapt...
Abstract. Every K-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Marti...
AbstractThe set A is low for (Martin-Löf) randomness if each random set is already random relative t...
We compare various notions of algorithmic randomness. First we consider relativized randomness. A s...
Let R be a notion of algorithmic randomness for individual subsets of N. We say B is a base for R ra...
We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study ...
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
Abstract. A relatively longstanding question in algorithmic randomness is Jan Reimann’s question whe...
The set A is low for Martin-Lof random if each random set is already random relative to A. A is K-t...
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...
Abstract. We say that A ≤LR B if every B-random number isA-random. Intuitively this means that if or...
Abstract. We compare various notions of algorithmic randomness. First we consider relativized random...
We say that A≤LRB if every B-random number is A-random. Intuitively this means that if oracle A can ...
Abstract. Every K-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Marti...
This thesis establishes results in several different areas of computability theory. The first chapt...
Abstract. Every K-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Marti...
AbstractThe set A is low for (Martin-Löf) randomness if each random set is already random relative t...
We compare various notions of algorithmic randomness. First we consider relativized randomness. A s...
Let R be a notion of algorithmic randomness for individual subsets of N. We say B is a base for R ra...
We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study ...
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
Abstract. A relatively longstanding question in algorithmic randomness is Jan Reimann’s question whe...
The set A is low for Martin-Lof random if each random set is already random relative to A. A is K-t...