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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It also sets up Model Theory nicely and has a brief intro to modal logic. Chapters would have made Model Theory quite a bit easier to tackle. Lattice Representations for Computability Theory.
For me, though, it was on the easy side. If you’re not familiar with the concept, this chapter is a great introduction. After putting down Cpmputability Theory partway through I picked up a book on logic.
G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers
Preview — Computability and Logic by George S. Just a moment while we sign you in to your Goodreads account. Assumming little background knowledge, it has been incredibly satisfying to be shown how various computational systems work, and then also to show that they’re equivalent. A vast improvement over the fourth edition. 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 persp Written for an audience with little more background in Math than the absolute basics of Set Theory probably reading the Enderton book on Set Theory is enough prep for this one, and that’s a very light readit casts a great many interesting theorems in Logic and Computability as so many instances of the non-enumerability of the reals.
Computability and Logic by George S. Boolos
Nov 24, Correy rated it really liked it. This book is a great way to shore up your understanding of some of the most fun proofs in computability theory and in logic. These four functions are called the “primitive recursive” functions, and some time is spent exploring what they can do. Computability and Logic by George S. However, the 4th edition is plagued with serious typographic errors in the exercises. This chapter introduces provability logic and is the reason I picked up lofic textbook, initially.
I’m reviewing the books on the MIRI course ,ogic.
If anyone else is thinking of reading the course list, Computability and Logic is compurability great place to start. This leads to a discussion of the “size” of infinite sets, which can be somewhat surprising the first time through.
Jun 22, Warunika Ranaweera rated it it was amazing. It even feels nice — it’s got thick pages, large text, and a number of useful diagrams.
You should definitely read chapters if you get the chance, computabilitj if you’re not already familiar with the bridge between Turing machines and recursive functions. Including anx 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 annd 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.
Bookhead rated it really liked it May 18, As before, this is an awesome way to get a hands-on feel for a theoretical result that is commonly acknowledged but seldom explored. They’re a great way to brush up on your understanding of incompleteness, if you think you have to. The subject matter may start out bolox little basic for much of the audience I expect people who approach the course list to already know enumerability, the halting problem, etc.
Jeffrey – – Bulletin of Symbolic Logic 9 4: Emily rated it really liked it Sep 18, John Burgess has a list boloos corrections on his website, but it is better just to buy the corrected fifth edition. Adam Gardner rated it really liked it Dec 21, It spent quite a bit of time motivating and fleshing out concepts that Model Theory dumps on your head.
Book Review: Computability and Logic
Cmputability and relations are called “primitive recursive” if their indicator functions can be constructed from primitive recursive building blocks. This is a fun chapter to read if you feel like exploring the boundaries of undecidability. It’s not a very in-depth introduction. Yasser Dawood rated it really liked it Feb 08, Laurie Wilkes rated it liked it Mar 12, Note that the indicator function for recursive sets must be total — i. From there, indefinability, undecidability, and incompleteness are just a hop, skip, and jump away.
Again, if this sounds new, I highly recommend picking up Computability and Logic: Andrada Pop rated it it was amazing Mar 31, By this measure, the following sets are the same size:. Jeffrey Ketland – – Analysis 66 4: You should probably pick up a book on how to effectively, and elegantly, write a proof before reading this.
This closes anr loop: This book excels at showing you the actual mechanisms behind results that are often mentioned but seldom exposed. Chapters also come highly recommended if you want to really understand incompleteness and undecidability.
Cambridge University Press, Cambridge, If you’ve never experienced such an encoding before, this chapter is a fun read: This involves developing a numeric encoding of first-order formulas, and recursive functions that can manipulate formulas so encoded.
Dec 06, Chris Rhodes rated it really liked it Shelves: Several proofs are, in fact, impossible. Read the ones that seem interesting, but don’t be afraid to skip the ones that seem boring.