The degrees of unsolvability provide a way to study the continuum in algorithmic terms. Measure and category, on the other hand, provide notions of size for subsets of the continuum, giving rise to corresponding notions of “typicality” for real numbers. We give an overview of the order-theoretic properties of the degrees of typical reals, presenting old and recent results, and pointing to a number of open problems for future research on this topic
On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I
"The first edition of this book appeared in 1905 as a reprint from the Annals of mathematics, series...
This book addresses a number of questions in real analysis and classical measure theory that are of ...
1 Introduction Recently there has been exciting progress in our understanding of algorithmicrandomne...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998.We focus on the A° sets and s...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998.We focus on the A° sets and s...
We discuss mathematical and physical arguments contrasting continuous and discrete, limitless discre...
Two classic “phase transitions” in discrete mathematics are the emergence of a giant component in a ...
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
Two classic “phase transitions” in discrete mathematics are the emergence of a giant component in a ...
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
This paper was initially submitted for the Oberwolfach special issue in which it had been accepted a...
Abstract. We study the approximation properties of computably enumerable reals. We deal with a natur...
AbstractWe show that there exists a real α such that, for all reals β, if α is linear reducible to β...
The isolation of dimensions from a data matrix has been traditionally formulated in terms of an al-g...
On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I
"The first edition of this book appeared in 1905 as a reprint from the Annals of mathematics, series...
This book addresses a number of questions in real analysis and classical measure theory that are of ...
1 Introduction Recently there has been exciting progress in our understanding of algorithmicrandomne...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998.We focus on the A° sets and s...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998.We focus on the A° sets and s...
We discuss mathematical and physical arguments contrasting continuous and discrete, limitless discre...
Two classic “phase transitions” in discrete mathematics are the emergence of a giant component in a ...
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
Two classic “phase transitions” in discrete mathematics are the emergence of a giant component in a ...
The Turing degree of a real measures the computational difficulty of producing its binary expansion....
This paper was initially submitted for the Oberwolfach special issue in which it had been accepted a...
Abstract. We study the approximation properties of computably enumerable reals. We deal with a natur...
AbstractWe show that there exists a real α such that, for all reals β, if α is linear reducible to β...
The isolation of dimensions from a data matrix has been traditionally formulated in terms of an al-g...
On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I
"The first edition of this book appeared in 1905 as a reprint from the Annals of mathematics, series...
This book addresses a number of questions in real analysis and classical measure theory that are of ...