Rating: 0 out of 5 stars
0 ratings
Ebook633 pages18 hours
Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers
By P. Odifreddi
Rating: 0 out of 5 stars
()
About this ebook
1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles.
Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
Related to Classical Recursion Theory
Titles in the series (32)
Problems in the Philosophy of Mathematics Recursive Model Theory Rating: 5 out of 5 stars5/5Boole's Logic and Probability: A Critical Exposition from the Standpoint of Contemporary Algebra, Logic and Probability Theory Rating: 0 out of 5 stars0 ratingsLogic Colloquium '85 Rating: 0 out of 5 stars0 ratingsHandbook of Mathematical Logic Rating: 4 out of 5 stars4/5Topoi: The Categorial Analysis of Logic Rating: 5 out of 5 stars5/5Model Theory Rating: 0 out of 5 stars0 ratingsThe Lambda Calculus: Its Syntax and Semantics Rating: 5 out of 5 stars5/5Foundations of Set Theory Rating: 0 out of 5 stars0 ratingsEquivalents of the Axiom of Choice, II Rating: 0 out of 5 stars0 ratingsIntensional Mathematics Rating: 0 out of 5 stars0 ratingsDescriptive Set Theory Rating: 5 out of 5 stars5/5Set Theory An Introduction To Independence Proofs Rating: 4 out of 5 stars4/5Computability, Complexity, Logic Rating: 0 out of 5 stars0 ratingsClassical Recursion Theory: The Theory of Functions and Sets of Natural Numbers Rating: 0 out of 5 stars0 ratingsCombinatorial Set Theory: Partition Relations for Cardinals Rating: 0 out of 5 stars0 ratingsLogic Colloquium '86 Rating: 0 out of 5 stars0 ratingsLanguage in Action: Categories, Lambdas and Dynamic Logic Rating: 0 out of 5 stars0 ratingsHarvey Friedman's Research on the Foundations of Mathematics Rating: 0 out of 5 stars0 ratingsLogic Colloquium '88 Rating: 0 out of 5 stars0 ratingsLogic Colloquium '87 Rating: 0 out of 5 stars0 ratingsLogical Frameworks for Truth and Abstraction: An Axiomatic Study Rating: 0 out of 5 stars0 ratingsLogic, Methodology and Philosophy of Science VIII Rating: 0 out of 5 stars0 ratingsLogic, Methodology and Philosophy of Science IX Rating: 0 out of 5 stars0 ratingsAdmissibility of Logical Inference Rules Rating: 0 out of 5 stars0 ratingsRecursive Functionals Rating: 0 out of 5 stars0 ratingsHausdorff Gaps and Limits Rating: 0 out of 5 stars0 ratingsLectures on the Curry-Howard Isomorphism Rating: 0 out of 5 stars0 ratingsRudiments of Calculus Rating: 0 out of 5 stars0 ratingsComputable Structures and the Hyperarithmetical Hierarchy Rating: 0 out of 5 stars0 ratings
Related ebooks
Recursive Functionals Rating: 0 out of 5 stars0 ratingsFinite Automata: Behavior and Synthesis Rating: 5 out of 5 stars5/5I: Functional Analysis Rating: 4 out of 5 stars4/5Language in Action: Categories, Lambdas and Dynamic Logic Rating: 0 out of 5 stars0 ratingsMathematical Modelling Techniques Rating: 3 out of 5 stars3/5Foundations of Genetic Algorithms 1991 (FOGA 1) Rating: 0 out of 5 stars0 ratingsAlgebra, Topology, and Category Theory: A Collection of Papers in Honor of Samuel Eilenberg Rating: 5 out of 5 stars5/5Handbook of Mathematical Logic Rating: 4 out of 5 stars4/5Real Reductive Groups I Rating: 0 out of 5 stars0 ratingsRecursive Analysis Rating: 0 out of 5 stars0 ratingsGeneral Theory of Markov Processes Rating: 0 out of 5 stars0 ratingsHilbert Spaces Rating: 0 out of 5 stars0 ratingsIntroduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements Rating: 0 out of 5 stars0 ratingsMathematical Logic Rating: 5 out of 5 stars5/5Finite Dimensional Vector Spaces. (AM-7), Volume 7 Rating: 4 out of 5 stars4/5Infinite Abelian Groups Rating: 0 out of 5 stars0 ratingsFourier Analysis in Probability Theory Rating: 0 out of 5 stars0 ratingsThe Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order Rating: 0 out of 5 stars0 ratingsGraph Theory Rating: 5 out of 5 stars5/5Introduction to Abstract Analysis Rating: 0 out of 5 stars0 ratingsElements of the Theory of Functions Rating: 4 out of 5 stars4/5Ergodic Theory and Topological Dynamics Rating: 0 out of 5 stars0 ratingsThe Aim and Structure of Physical Theory Rating: 4 out of 5 stars4/5Applied Finite Mathematics Rating: 5 out of 5 stars5/5Lectures on Ordinary Differential Equations Rating: 4 out of 5 stars4/5Classical and Modern Integration Theories Rating: 1 out of 5 stars1/5Proof Theory: Second Edition Rating: 0 out of 5 stars0 ratings
Systems Architecture For You
CompTIA A+ CertMike: Prepare. Practice. Pass the Test! Get Certified!: Core 1 Exam 220-1101 Rating: 0 out of 5 stars0 ratingsEmbedded Hardware: Know It All Rating: 5 out of 5 stars5/5CompTIA ITF+ CertMike: Prepare. Practice. Pass the Test! Get Certified!: Exam FC0-U61 Rating: 0 out of 5 stars0 ratingsRaspberry Pi Projects For Dummies Rating: 5 out of 5 stars5/5CompTIA Network+ CertMike: Prepare. Practice. Pass the Test! Get Certified!: Exam N10-008 Rating: 0 out of 5 stars0 ratingsSolution Architecture Foundations Rating: 3 out of 5 stars3/5Computer Science: A Concise Introduction Rating: 4 out of 5 stars4/5.NET Core in Action Rating: 0 out of 5 stars0 ratingsBlockchain Basics: A Non-Technical Introduction in 25 Steps Rating: 5 out of 5 stars5/5Wii U Architecture: Architecture of Consoles: A Practical Analysis, #21 Rating: 0 out of 5 stars0 ratingsAdvanced API Security: OAuth 2.0 and Beyond Rating: 0 out of 5 stars0 ratingsLearning Ansible 2 - Second Edition Rating: 5 out of 5 stars5/5Xbox 360 Architecture: Architecture of Consoles: A Practical Analysis, #20 Rating: 0 out of 5 stars0 ratingsMastering Kubernetes Rating: 5 out of 5 stars5/5Raspberry Pi User Guide Rating: 4 out of 5 stars4/5Arduino Projects For Dummies Rating: 3 out of 5 stars3/5DevOps for Web Development Rating: 0 out of 5 stars0 ratingsDistributed Facts Device for Flow Controls Rating: 0 out of 5 stars0 ratingsSAP Security Configuration and Deployment: The IT Administrator's Guide to Best Practices Rating: 0 out of 5 stars0 ratingsSoftware Architecture with Python Rating: 0 out of 5 stars0 ratingsWii Architecture: Architecture of Consoles: A Practical Analysis, #11 Rating: 0 out of 5 stars0 ratingsLearn Git in a Month of Lunches Rating: 0 out of 5 stars0 ratingsXbox Architecture: Architecture of Consoles: A Practical Analysis, #13 Rating: 0 out of 5 stars0 ratingsThe IT Support Handbook: A How-To Guide to Providing Effective Help and Support to IT Users Rating: 0 out of 5 stars0 ratingsSNES Architecture: Architecture of Consoles: A Practical Analysis, #4 Rating: 0 out of 5 stars0 ratingsComputer System Organization: The B5700/B6700 Series Rating: 0 out of 5 stars0 ratingsFault-Tolerant Systems Rating: 0 out of 5 stars0 ratings
Related podcast episodes
1. Improvisation 2. Innovation 3. Imitation 0% found this document useful19: Molecules in 3D 0% found this document usefulWas Einstein Wrong?? 0% found this document usefulDarsh Kodwani Astrophysicist Episode 16 0% found this document usefulCarlo Rovelli: From Dante to White Holes 0% found this document usefulBonus : The Perils of Science Communication: Where do we draw the line between Outreach and Clickbait? 0% found this document usefulCarlo Rovelli: Quantum Weirdness!?: Carlo Rovelli: Quantum Weirdness!? 0% found this document usefulArchitects of the underworld: A conversation with Dr. Walter Tschinkel 0% found this document useful
Related articles
Euclid as Founding Father: We hold this mathematics to be self evident. NautilusArticle
Euclid as Founding Father: We hold this mathematics to be self evident.
Oct 13, 2016
Despite the man’s awkward gestures, unkempt hair, and ill-fitting suit, it was one of the most extraordinary speeches that Reverend John Gulliver had ever heard. It was March 1860, and the venue was Norwich, Connecticut. The following morning Gullive
8 min read“There’s No Single ‘Best’ Language To Learn. I Think The Real Key Is To Learn How To Write Code” PC Pro MagazineArticle
“There’s No Single ‘Best’ Language To Learn. I Think The Real Key Is To Learn How To Write Code”
Oct 8, 2022
9 min readAPL: Going Strong After All These Years Linux FormatArticle
APL: Going Strong After All These Years
Mar 7, 2023
Mike Bedford might not use it in anger, but he’s been fascinated by APL’s quirkiness since he first saw how it could generate prime numbers in just 20 characters. The abandonment of strange symbols in later Iversonian languages, such as J and K, has
11 min readPhysicists Attack Math’s $1,000,000 Question QuantaArticle
Physicists Attack Math’s $1,000,000 Question
Apr 4, 2017
Physicists are attempting to map the distribution of the prime numbers to the energy levels of a particular quantum system.
4 min readThe Fundamental Limits of Machine Learning NautilusArticle
The Fundamental Limits of Machine Learning
Aug 14, 2017
5 min readWe Need an FDA For Algorithms NautilusArticle
We Need an FDA For Algorithms
Nov 1, 2018
In the introduction to her new book, Hannah Fry points out something interesting about the phrase “Hello World.” It’s never been quite clear, she says, whether the phrase—which is frequently the entire output of a student’s first computer program—is
10 min readHow the Slowest Computer Programs Illuminate Math’s Fundamental Limits QuantaArticle
How the Slowest Computer Programs Illuminate Math’s Fundamental Limits
Dec 10, 2020
6 min readMath After COVID-19 QuantaArticle
Math After COVID-19
Apr 28, 2020
4 min readSmaller Is Better: Why Finite Number Systems Pack More Punch QuantaArticle
Smaller Is Better: Why Finite Number Systems Pack More Punch
Feb 11, 2019
4 min readMost Tech Today Would be Frivolous to Ancient Scientists NautilusArticle
Most Tech Today Would be Frivolous to Ancient Scientists
Apr 19, 2019
5 min readLessons For A Young Scientist NautilusArticle
Lessons For A Young Scientist
Jan 12, 2022
I sometimes worry that many who would enjoy a scientific career are put off by a narrow and outdated conception of what’s involved. The word “scientist” still conjures up an unworldly image of an Einstein lookalike (male and elderly) or else a youthf
8 min readLessons For A Young Scientist NautilusArticle
Lessons For A Young Scientist
Jan 9, 2020
I sometimes worry that many who would enjoy a scientific career are put off by a narrow and outdated conception of what’s involved. The word “scientist” still conjures up an unworldly image of an Einstein lookalike (male and elderly) or else a youthf
7 min readTo Defend Western Civilization, Start With Science NPRArticle
To Defend Western Civilization, Start With Science
Jul 18, 2017
3 min readDo You Know These Scientific Pioneers? NautilusArticle
Do You Know These Scientific Pioneers?
Nov 25, 2020
It’s easy to name science and math geniuses. I can just flip open my old book from the 1960s, which lists “100 Great Scientists”; it contains all the names you’d find on most popular lists of scientific geniuses: Einstein, Newton, Maxwell, Gauss, Boh
5 min readHere’s Our Cutting-Edge, Crowdsourced Imaginary Time Capsule NautilusArticle
Here’s Our Cutting-Edge, Crowdsourced Imaginary Time Capsule
Jan 31, 2014
2 min readSuperflex Uses Humor to Challenge Corporate Power NewsweekArticle
Superflex Uses Humor to Challenge Corporate Power
Jun 9, 2017
4 min readHow to Build a Search Engine for Mathematics: The Surprising Power of Neil Sloane’s Encyclopedia of Integer Sequences.: The surprising power of Neil Sloane’s Encyclopedia of Integer Sequences. NautilusArticle
How to Build a Search Engine for Mathematics: The Surprising Power of Neil Sloane’s Encyclopedia of Integer Sequences.: The surprising power of Neil Sloane’s Encyclopedia of Integer Sequences.
Oct 22, 2015
On the average summer Saturday, the mathematician Neil Sloane woke up to a crisis. “There are always crises,” he said— albeit crises of the teapot tempest variety. One Saturday over breakfast, he faced an inbox message titled “edits from outer space.
10 min readThe Termite and the Architect: Animal Homes Resist Our Understanding.: Animal homes resist our understanding. NautilusArticle
The Termite and the Architect: Animal Homes Resist Our Understanding.: Animal homes resist our understanding.
Dec 26, 2013
In 1991, the multinational Old Mutual investment group approached the Zimbabwean architect Mick Pearce with an audacious assignment. The group wished to construct a retail and office complex called the Eastgate Centre in Zimbabwe’s capital city of Ha
10 min readThe Joy of Condensed Matter NautilusArticle
The Joy of Condensed Matter
Feb 24, 2021
Everyone seems to be talking about the problems with physics: Peter Woit’s book Not Even Wrong, Lee Smolin’s The Trouble With Physics, and Sabine Hossenfelder’s Lost in Math leap to mind, and they have started a wider conversation. But is all of phys
7 min readGalileo And The Telescope TechfastlyArticle
Galileo And The Telescope
May 3, 2021
If you were to ever find yourself strolling through the Mueseo Galileo in the city of Florence, Italy, you would likely chance upon a rather ordinary object. At least, that’s what it looks like at first glance. Do give it a second peek, as this relic
1 min readIs It Time to Embrace Unverified Theories? NautilusArticle
Is It Time to Embrace Unverified Theories?
Aug 11, 2015
4 min readGulliver’s Travels PEARLArticle
Gulliver’s Travels
Oct 30, 2018
5 min readWhy Mathematicians Should Stop Naming Things After Each Other NautilusArticle
Why Mathematicians Should Stop Naming Things After Each Other
Sep 2, 2020
Any student of modern math must know what it feels like to drown in a well of telescoping terminology. For a high-profile example, let’s take the Calabi-Yau manifold, made famous by string theory. A Calabi-Yau manifold is a compact, complex Kähler ma
6 min readTop Ten Unsung Geniuses: For these scientists, success and fame did not come in equal measure. NautilusArticle
Top Ten Unsung Geniuses: For these scientists, success and fame did not come in equal measure.
Oct 16, 2014
It’s easy to name science and math geniuses. I can just flip open my old book from the 1960s, which lists “100 Great Scientists”; it contains all the names you’d find on most popular lists of scientific geniuses: Einstein, Newton, Maxwell, Gauss, Boh
5 min readWhat Is a Beautiful Experiment? NautilusArticle
What Is a Beautiful Experiment?
Aug 11, 2023
6 min readQuantum Mechanics 101 All About SpaceArticle
Quantum Mechanics 101
Dec 5, 2019
7 min readDid You Know? How It WorksArticle
Did You Know?
Sep 5, 2019
4 min readQuark Of Habit The American ScholarArticle
Quark Of Habit
Dec 1, 2022
A round 400 BC, the Greek philosopher Democritus proffered the idea that all matter was composed of indivisible, featureless constituents. He described them using the Greek word for “uncuttable”: atomos. Two thousand years later, scientists found tha
4 min readInfinite Energy New PhilosopherArticle
Infinite Energy
Apr 19, 2021
11 min readThe Math of Living Things NautilusArticle
The Math of Living Things
Jun 23, 2021
It’s hard to argue with the famously authoritative Oxford English Dictionary, but its definition of physics as the “branch of science concerned with the nature and properties of non-living matter and energy” is incomplete because physics studies livi
8 min read
Reviews for Classical Recursion Theory
Rating: 0 out of 5 stars
0 ratings
0 ratings0 reviews
Book preview
Classical Recursion Theory - P. Odifreddi
Enjoying the preview?
Page 1 of 1