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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G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers
We now move to the loigc topics” section of the book. It has lots of diagrams and gives you a good feel for what sort of power an “abacus machine” something that can do real math has as a computational engine. This chapter introduces Ramsey’s theorem a result in combinatorics and uses it to obtain an undecidable sentence that doesn’t do any overt diagonalization.
But if the theorem has always seemed somewhat confusing to you even after the cartoon guide then this chapter may well be enlightening. This chapter left me a bit unsatisfied. If you like books and love to build cool products, we may be looking for you.
Computability and Logic by George S. Boolos
This entry has no external links. If you’ve never experienced such an encoding before, this chapter is a fun read: The result is shown in this chapter by elimination of quantifiers: Nad smoothly unifies diagonalization with the intuitive impossibility of the halting problem.
This chapter introduces enumerability, and some of the cooler results.
It’s a tool for finding a set that defies a given encoding. This is another interesting exploration of the boundaries of undecidability. Lewis Cawthorne rated computabolity liked it Jun 28, This is the classic textbook for anyone who wants to study logic up to and beyond Godel.
It’s good clean fun ccomputability see these things play out in front of you, instead of just hearing the results secondhand. I plan to explore this subject more in my free time.
Book Review: Computability and Logic
This chapter shows that a function is recursive iff it is Turing computable. Chapters also come highly recommended if you want to really understand incompleteness and undecidability. This book wasn’t the most useful book I’ve read in this series.
Sets and relations are called “primitive recursive” if their indicator functions can be computabiloty from primitive recursive building blocks.
We can actually make that stronger: Open Preview See a Problem? It’s very interesting to see how much is equivalent to that one fact, but I also can’t help but feel that some of the proofs could benefit from a different perspective. This chapter is entirely devoted to a proof of the compactness theorem. The chapter then discusses formal systems of arithmetic.
That said, I didn’t find it very useful to me personally. This is ,ogic mechanism by which we will embed arithmetic in itself. Diagonalization is incredibly important if you want to play with infinities or learn about decidability. Andrew rated it it was amazing Apr 22, The second chapter of Computability and Logic is a clever and easy introduction to diagonalization, and I highly recommend it to newcomers. Still, while this book was not exactly what I needed, Llogic highly recommend it for other purposes.
Andrada Pop rated it it was amazing Mar 31, This chapter introduces another formalism that has more machinery available to it than a Turing machine. Adam Gardner rated it really liked it Dec 21, Books by George S. It is a solid introduction to the concepts. This involves developing loigc numeric encoding of first-order formulas, and recursive functions that can manipulate formulas so encoded. Eric Casteleijn rated it liked it Jun 27, I highly recommend reading this book before Model Theoryif you’re planning to read both.
The turing machine chapters are decent. Assumming little background knowledge, it has been incredibly satisfying to be shown how various computational systems work, and then also loggic show that they’re equivalent. It could be an invaluable resource for anyone in computer science looking to branch out into logic.
In fact, I planned to skim the first two sections up through chapter