9 edition of Recursive function theory and logic. found in the catalog.
Recursive function theory and logic.
Bibliography: p. 321-326.
|Series||Computer science and applied mathematics|
|LC Classifications||QA248.5 .Y36|
|The Physical Object|
|Pagination||xv, 338 p.|
|Number of Pages||338|
|LC Control Number||74154379|
In this volume, the tenth publication in the Perspectives in Logic series, Jens E. Fenstad takes an axiomatic approach to present a unified and coherent account of the many and various parts of general recursion theory. The main core of the book gives an account of the general theory of computations. In mathematical logic and computer science, a general recursive function (often shortened to recursive function) or μ-recursive function, is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense. In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is .
Recursion (adjective: recursive) occurs when a thing is defined in terms of itself or of its ion is used in a variety of disciplines ranging from linguistics to most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances. The complexity theory of computable functions, which has flourished during the last 20 years, is only touched upon, but most research papers in that area implicitly rely on the ideas and results in this book. Readers may wish to consult a more recent treatment of recursion theory by Soare .
Since the recursive functions are of fundamental importance in logic and computer science, it is a natural pure-mathematical exercise to attempt to classify them in some way according to their logical and computational complexity. We hope to convince the reader that this is also an interesting and a useful thing to do: interesting because it brings to bear, in a clear and simple context, some. Volume II of Classical Recursion Theory describes the universe from a local (bottom-upor synthetical) point of view, and covers the whole spectrum, from therecursive to the arithmetical first half of the book provides a detailed picture of the computablesets from the perspective of Theoretical Computer Science. Besides giving adetailed description of the theories of abstract.
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This book is a mathematical, but not at all fully rigorous textbook on computability and recursive functions in 12 chapters on much of the standard theory. Nigel Cutland is/was a professor of 'pure' mathematics, hence the strongly mathematical by: Recursive Function Theory and Logic (Computer science and applied mathematics) First Edition by Ann Yasuhara (Author) › Visit Amazon's Ann Yasuhara Page.
Find all the books, read about the author, and more. See search results for this author. Are Cited by: Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol.
2 (Studies in Logic and the Foundations of Mathematics, Vol. ) (Volume ) P. Cited by: Additional Physical Format: Online version: Yasuhara, Ann. Recursive function theory and logic. New York, Academic Press  (OCoLC) Material Type. Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol.
1 (Studies in Logic and the Foundations of Mathematics, Vol. ) (Volume ) Piergiorgio Odifreddi. out of 5 stars 3. Paperback.
$ Computability: An Introduction to Recursive Function TheoryCited by: 9. Other articles where Recursion theory is discussed: history of logic: Theory of recursive functions and computability: In addition to proof theory and model theory, a third main area of contemporary logic is the theory of recursive functions and computability.
Much of the specialized work belongs as much to computer science as to logic. The origins. Theory of recursive functions and computability. In addition to proof theory and model theory, a third main area of contemporary logic is the theory of recursive functions and computability.
Much of the specialized work belongs as much to computer science as to logic. The origins of recursion theory nevertheless lie squarely in logic. Volume II of Classical Recursion Theory describes the universe from a local (bottom-upor synthetical) point of view, and covers the whole spectrum, from therecursive to the arithmetical sets.
The first half of the book provides a detailed picture of the computablesets from the perspective of Theoretical Computer Science. Besides giving adetailed description of the theories of abstract. Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the s with the study of computable functions and Turing field has since expanded to include the study of generalized computability and these areas, recursion theory overlaps with proof theory and.
Recursive function theory, like the theory of Turing machines, is one way to make formal and precise the intuitive, informal, and imprecise notion of an effective method. It happens to identify the very same class of functions as those that are Turing computable.
Reviews. Hartley Rogers Jr., Theory of Recursive Functions and Effective Computability. McGraw-Hill Book Company, New York, St. Louis, San Francisco, Toronto, London. History of logic - History of logic - Applications of recursive-function theory: Questions about effective computability come up naturally in different contexts.
Not surprisingly, recursive-function theory has developed in different directions and has been applied to different problem areas. The recursive unsolvability of the decision problem for first-order logic illustrates one kind of.
In computability theory, a primitive recursive function is roughly speaking a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop can be determined before entering the loop).
Primitive recursive functions form a strict subset of those general recursive functions that are also total functions.
Odifreddi, Piergiogio,Classical Recursion Theory. volume 1: The Theory of Functions and Sets of Natural Numbers, (Studies in Logic and the Foundations of Mathematics ), Amsterdam: North-Holland –––, a, Classical Recursion Theory. volume 2, (Studies in Logic and the Foundations of Mathematics ), Amsterdam: North-Holland.
Herbert B. Enderton, in A Mathematical Introduction to Logic (Second Edition), Recursive Functions. We have used recursive functions (i.e., functions that, when viewed as relations, are recursive) to obtain theorems of incompleteness and undecidability of theories.
But the class of recursive functions is also an interesting class in its own right, and in this section we will indicate a. Structure. The courses in logic at Harvard cover all of the major areas of mathematical logic—proof theory, recursion theory, model theory, and set theory—and, in addition, there are courses in closely related areas, such as the philosophy and foundations of mathematics, and theoretical issues in the theory of computation.
Recursive function theory and logic. [Ann Yasuhara] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Contacts Search for a Library.
Create Book\/a>, schema:CreativeWork\/a> ; \u00A0\u00A0\u00A0\n library. Hartry Field - - Journal of Philosophical Logic 32 (2) Squeezing Arguments.
Similar books and articles. Computability, an Introduction to Recursive Function Theory. Nigel Cutland - - Cambridge University Press. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians).
Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory 5/5(2).
The book introduces the theory of computability and non-computability to the mathematically-comfortable. The theory of recursive functions provides entry to that theoretical territory at the limits of what is computable and what is s:. Many of the original books in the series have been unavailable for years, but they are now in print once again.
The theory set out in this volume, the ninth publication in the Perspectives in Logic series, is the result of the meeting and common development of two currents of mathematical research: descriptive set theory and recursion theory.Theory of Recursive Functions and Effective Computability | Hartley Rogers | download | B–OK.
Download books for free. Find books.Recursive functions are common in computer science because they allow programmers to write efficient programs using a minimal amount of code.
The downside is that they can cause infinite loops and other unexpected results if not written properly. For example, in the example above, the function is terminated if the number is 0 or less or greater.