*Frontmatter, pg. i*TABLE OF CONTENTS, pg. iii*PREFACE, pg. vii*ANNALS OF MATHEMATICS STUDIES, pg. xiv*CHAPTER I: FORMAL MATHEMATICAL SYSTEMS, pg. 1*CHAPTER II: FORMAL REPRESENTABILITY AND RECURSIVE ENUMERABILITY, pg. 19*CHAPTER III: INCOMPLETENESS -AND UNDECIDABILITY, pg. 39*CHAPTER IV: RECURSIVE FUNCTION THEORY, pg. 65*CHAPTER V: CREATIVITY AND EFFECTIVE INSEPARABILITY, pg. 93*SUPPLEMENT: APPLICATIONS TO MATHEMATICAL LOGIC, pg. 127*REFERENCE AND BRIEF BIBLIOGRAPHY, pg. 141