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I'm trying to understand the sorts of things found on this page: http://ncatlab.org/nlab/show/realizability

In particular, I want to read Oosten's Realizability: An Introduction to the Categorical Side, and in the preface he wants me to know logic up to Godel's completeness theorem (I have this and more), category theory including topos theory (I sort of have this), and recursion theory (I don't have this at all).

Question 1: Where can I learn recursion theory for the purpose of reading Oosten?

Question 2 (to make the question more generally useful): What is a general roadmap to understanding the effective topos, assuming only basic classical logic and basic category theory?

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For recursion theory you can read the first chapters of Boolos & Jefferey "Computability and Logic" or S. B. Cooper's "Computability Theory".

I think a good starting point for understanding the categorical realizability would be T. Streicher's lecture notes

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