Download or read book Some Results One genericity and Recursively Enumerable Weak Truth Table Degrees written by Richard Warren Blaylock and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this manuscript we explore two topics in recursion theory and their interaction. The first topic is e-genericity, a notion of genericity for recursively enumerable (r.e.) sets introduced by C. G. Jockusch, Jr. The second is weak truth table reducibility (w-reducibility), a strong reducibility (i.e., stronger than the most general Turing reducibility) first introduced by Friedberg and Rogers. In Chapter 1 we give a brief introduction to these topics and establish the relevant terminology and notation. In Chapter 2 we give some closure and non-closure properties for the classes of e-generic sets and degrees, which are predicted by analogous results for previous notions of genericity. For example, the e-generic sets are not closed under union, intersection, or join, but on the other hand if the join $A oplus B$ of two sets is e-generic, then so are $A,B, A cup B$, and $A cap B$. In Chapter 3 we investigate the structure of the weak truth table degrees (w-degrees) inside an e-generic Turing degree. Here we show that e-generic Turing degrees are highly noncontiguous in the sense that they contain no greatest and no least r.e. w-degree. Finally in Chapter 4 we obtain some results on the ordering of the r.e. w-degrees in general. The main result is the existence of a nontrivial r.e. w-degree a which has a greatest lower bound with every r.e. w-degree b. We also show that these nontrivial completely cappable degrees can neither be low nor promptly simple.

Download or read book Some Results on E genericity and Recursively Enumerable Weak Truth Table Degrees written by Richard Warren Blaylock and published by . This book was released on 1991 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Turing and Truth Table Degrees of 1 generic and Recursively Enumerable Sets written by Christine Ann Haught and published by . This book was released on 1985 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Recursively Enumerable Sets and Degrees written by Robert I. Soare and published by Springer Science & Business Media. This book was released on 1999-11-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: ..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988

Download or read book Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees written by Rodney G. Downey and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.

Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dissertation Abstracts International written by and published by . This book was released on 1992 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1990 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Computability Theory written by E.R. Griffor and published by Elsevier. This book was released on 1999-10-01 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.

Download or read book The Philosopher s Index written by and published by . This book was released on 1990 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1969- include a section of abstracts.

Download or read book American Doctoral Dissertations written by and published by . This book was released on 1991 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computable Structure Theory written by Antonio Montalbán and published by Cambridge University Press. This book was released on 2021-06-24 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.

Download or read book A Hierarchy of Turing Degrees written by Rod Downey and published by Princeton University Press. This book was released on 2020-06-16 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Alpha]-c.a. functions -- The hierarchy of totally [alpha]-c.a. degrees -- Maximal totally [alpha]-c.a. degrees -- Presentations of left-c.e. reals -- m-topped degrees -- Embeddings of the 1-3-1 lattice -- Prompt permissions.

Download or read book Referativny zhurnal written by and published by . This book was released on 1986 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Slicing The Truth On The Computable And Reverse Mathematics Of Combinatorial Principles written by Denis R Hirschfeldt and published by World Scientific. This book was released on 2014-07-18 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.

Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1989 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computability and Randomness written by André Nies and published by OUP Oxford. This book was released on 2012-03-29 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.