title: Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers, Vol. 1 (Studies in Logic and the Foundations of Mathematics, Vol. 125)
author: Piergiorgio Odifreddi
description: G.E. Sacks, Harvard University and M.I.T.<br />Odifreddi has written a delightful yet scholarly treatise...<br /> <br />C. Calude<br />An impressive presentation of classical recursion theory... highly recommended to everyone interested in recursion theory.<br />Zentralblatt fr Mathematik<br />A must as a reference manual for any mathematician, philosopher or theoretical computer scientist who deals with issues of computability.<br />Mathematical Reviews<br />An incredible wealth of information, including much that occurs for the first time in book form.<br />Journal of Symbolic Logic<br />
zlib_text: **ELEMENTARY RECURSION THEORY AND ITS APPLICATIONS**
  
   **TO FORMAL SYSTEMS**
  
   **By Professor Saul Kripke**
  
  Department of Philosophy, Princeton University
  
  Notes by Mario Gómez-Torrente,
  
  revising and expanding notes by John Barker
  
  Copyright © 1996 by Saul Kripke. Not for reproduction or quotation without
  express permission of the author.
  
  Elementary Recursion Theory. Preliminary Version Copyright © 1995 by Saul
  Kripke
  
   **CONTENTS**
  
   **Lecture I**
  
   **1**
  
  First Order Languages / Eliminating Function Letters / Interpretations / The
  Language of Arithmetic
  
   **Lecture II**
  
   **8**
  
  The Language RE / The Intuitive Concept of Computability and its Formal
  Counterparts / The Status of Church's Thesis
  
   **Lecture III**
  
   **18**
  
  The Language Lim / Pairing Functions / Coding Finite Sequences **Lecture IV**
  
  27
  
  Gödel Numbering / Identification / The Generated Sets Theorem / Exercises
  **Lecture V**
  
  36
  
  Truth and Satisfaction in RE
  
   **Lecture VI**
  
   **40**
  
  Truth and Satisfaction in RE (Co