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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Computability and Logic

There are no computabiljty topics on this book yet. I won’t ruin the fun here: This is interesting, because it shows us precisely where undecidability sets in.

If you’re interested in model theory, this is a great place to get a feel for the ideas. Nov 24, Correy rated it really liked it.

Book Review: Computability and Logic

This is where the magic happens. They are called “semirecursive” if there is a recursive function which at least says “yes” to elements that are in the set, even if it cannot say “no” to elements that are not in the set. It’s formal, but pulls off a conversational tone. When the authors finally introduce decidability sixty pages later it is not clearly compared with enumerability. This transition is motivated computationally: Cristian CaludeM. Thomas Schminke rated it really liked it Oct 22, Computability and Logicspecifically.


G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers

I highly recommend you familiarize yourself with these concepts at some point in your life, if only for fun. Sets and relations are called “primitive recursive” if their indicator functions can be constructed from primitive recursive building blocks.

View computabiliity 3 comments.

Cambridge University Press, Cambridge, Dec 06, Chris Rhodes rated it really liked it Shelves: For students boolls people in general who are extremely sophisticated mathematically, it can sometimes seem a little unrigorous. A Mathematical Introduction to Logic. British Journal for the Philosophy of Science 28 1: These four functions are called the “primitive recursive” functions, and some time is spent exploring what they can do. Cambridge University Press; 5 edition September 17, Language: It is a excelent book.

Several proofs are, in fact, impossible. Eric Casteleijn rated it liked it Jun 27, Even if you’re pretty comfortable with diagonalization, you may enjoy this chapter for its crisp treatment of the device.

They’re less polished and less motivated, and more likely to just dump a proof on you.


They are “recursive” if their indicator functions can be constructed from recursive building blocks. Request removal from index.

This result was surprising, and compytability proof is a fun one. Chapter 18 in particular is quite relevant to some of MIRI’s recent work, and is good to know in the LessWrong circles. This chapter introduces provability logic and is the reason I picked up this textbook, initially. Amazon Restaurants Food delivery from local restaurants.

Also, note that semirecursive sets are more commonly known as “recursively enumerable” sets. That said, I didn’t find it very useful to me personally. To ask other readers questions about Computability and Logicplease sign up. Jeffrey continue here in the tradition set by the late Boolos to present the “principal fundamental theoretical results logic” that would necessarily include the work of G del.

As before, this is an awesome way to get a hands-on feel for a theoretical result that is commonly acknowledged but seldom explored.