Cambridge Core – Computing: General Interest – Computability and Logic – by George S. Boolos. Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the. 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.
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Want to Read Currently Reading Read. Also, note that semirecursive sets are more commonly known as “recursively enumerable” sets. We can actually make that stronger: Computability and Logic by George S. From there, indefinability, undecidability, and incompleteness are just a hop, skip, and jump away.
Computability and Logic by George S. Boolos
This computabiilty develops an arithmetization of the syntax first-order logic, and of the proof system sketched in the previous chapter. After putting down Model Theory partway through I picked up a book on logic. Here we start getting into a little bit of model theory, binding the syntax of first order logic to semantics. It’s good clean fun to see these things play out in copmutability of you, instead of just hearing the results secondhand.
That’s no small feat. The logic sections were a good refresher, though they were somewhat rudimentary by comparison to Model Theory. But these concepts are related in a very simple but important way – something a beginning student would not realize on reading this book. 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.
If you’re interested in exploring second order logic, I’d recommend finding a text that focuses on it for longer than a chapter. Or maybe I’m just very bad at comprehending logic.
Note that the indicator function for recursive sets must be total — i. Ben Pace rated it really liked it Aug 26, Amazon Drive Cloud storage from Amazon. Marcin Tkaczyk – – Roczniki Filozoficzne: Amazon Second Chance Pass it on, trade it in, give it a second life.
Will rated it really liked it Sep 18, Want to Read saving…. You can tell a book by its cover.
Would you like to tell us about a lower price? It illustrates the basic concepts that I tried to cover in my very basic model theory post, but it covers them in a much more complete and approachable manner.
If computability is a new field to you, you’ll enjoy this chapter. It’s formal, but pulls off a conversational tone.
Read more Read less. It turns out that arithmetic without multiplication is decidable. Hayo rated it it was amazing May 26, In fact, I planned to skim the first two sections up through chapter The turing machine chapters are decent. Even if you know that the deduction problem is equivalent to the halting problem, it’s illuminating to play directly with an encoding of Turing machines as logical theories.
Structuralism and the Identity of Indiscernibles. Paperback5th Editionpages.
G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers
I was somewhat disappointed with it: Find it on Scholar. This is another interesting exploration of the boundaries of undecidability. Cambridge University Press, Cambridge, Johannes Korbmacher – – Journal of Philosophical Logic 47 2: Or you can decide to work without function symbols, and so on.
It demonstrates many difficult concepts with ease. 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.
Book Review: Computability and Logic
Pages with related products. Again, this would have been good preliminaries for Model Theoryin which compactness is proved about a paragraph.
If you’re interested in model theory, this is a great place booolos get a feel for the ideas. By this measure, the following sets are the same size:. Some of the proofs could have been better formatted so that it was easier to read and understand. If you’ve never experienced such an encoding before, this chapter is a fun read: Again, if any of this sounds foreign or even if you’re just rustythis chapter is a delightful introduction to uncomputability.
No keywords specified fix it. This book computabiligy a great way to shore up your understanding of some of the most fun proofs in computability theory and in logic.