Best introduction to recursive functions

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Hello I'm looking for a solid introduction to recursive functions within the domain of mathematical logic. I'm studying logic and would like to become more informed about this area of theory. I would appreciate any suggested texts.

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If I had to choose just one book, then it would probably be

Nigel Cutland, Computability: An Introduction to Recursive Function Theory (CUP 1980).

This is a rightly much-reprinted classic and is beautifully put together, even if (by now) perhaps just slightly old-school in "look-and-feel".

For more suggestions, you can take a look at The Teach Yourself Logic guide to the literature.

http://www.logicmatters.net/resources/pdfs/TeachYourselfLogic10-1.pdf

Check out §3.3 for introductory material on computable functions, and §5.5 for suggestions of rather more advanced texts.