Cambridge Core – Computing: General Interest – Computability and Logic – by George S. Boolos. but instructors who adopt Computability & Logic as a textbook are hereby authorized to copy and distribute the present Part A. This permission does not extend. Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the.
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This chapter is about formalizing a system of proofs. Including a selection of ex Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Turing’s theory of computability to Ramsey’s theorem.
If you’ve never played with nonstandard models before, this chapter is a nice introduction. Some of the proofs were blocks of text, and within them they would reference certain stages of the proof, but it wasn’t specified which ones, therefore the reader had to guess what part A B C was and where it’s subproof started.
Knowledge of enumerability is central to many issues in computer science, and is integral in any study of infinities. To see what your friends thought of this book, please sign up. It also sets up Model Theory nicely and has a brief intro to modal logic.
This is the classic textbook for anyone who wants to study logic up to and beyond Godel. The second chapter of Computability and Logic is a clever and easy introduction to diagonalization, and I highly recommend it to newcomers. This is one of my favorite results in mathematics, and it’s a beautiful and the original bridge between the lands of math and computer science. BoolosJohn P.
Computability and Logic
I was already quite comfortable with most of these subjects. It’s good clean fun to see these things play out in front of you, instead of just hearing the results secondhand. It also introduces the concepts of soundness and completeness.
This book is a great way to shore up your understanding of some of the most fun proofs in computability theory and in logic. This chapter actually shows you how to build a recursive function that computes the result of a Turing machine, and how to encode recursive functions as Turing-machine instructions. They’re a great way to brush up on your understanding of incompleteness, if you think you have to. Compactness is explained, but not proven.
Bolks smoothly unifies diagonalization with the intuitive impossibility of the halting problem. L rated it it was amazing Nov 30, Monthly downloads Sorry, there are not enough data points to plot this chart. It even feels nice — it’s got thick pages, large text, and a number of useful diagrams.
For those of you who don’t know, the Turing Machine is an idealized computation engine which can compute answers to a very large class of problems.
This chapter shows that a function is recursive iff it is Turing computable. Sign in to use this computabioity. If you’re interested in exploring second order logic, I’d recommend finding a text that focuses on it for longer than a chapter. The chapter even touches on the busy beaver problem. Sheeru rated it liked it Mar 15, That’s one thing I really like about this book: Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Loic theory of computability to Ramsey’s theorem.
If you’re not familiar with the concept, this chapter is a great introduction.
G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers
Science, Logic, and Mathematics categorize this paper. Rajeev Shrivastava rated it it was amazing Jan 13, It walks you through the implementation of a Turing machine, and shows you a number of clever algorithms by which a Turing machine computes simple algorithms. Also, note that semirecursive sets are more commonly known as “recursively enumerable” sets. Dec 06, Chris Rhodes rated it really liked it Shelves: It’s easy to get recursive and semirecursive sets mixed up, when you’re starting out.