Subrecursive hierarchies and provably computable functions in formal theories of arithmetic 帰納的関数の部分階層と数論の形式理論での証明可能な計算可能関数

博士論文

CONTENTS CHAPTER1 INTRODUCTION / p1 CHAPTER2 SUBRECURSIVE HIERARCHIES AND FORMAL THEORIES / p8 　2.1 Fast-growing hierarchy / p8 　2.2 Provable computability / p13 　2.3 Undecidable statements / p16 CHAPTER3 BUILT-UP SYSTEMS OF FUNDAMENTAL SEQUENCES / p19 　3.1 Growing hierarchies on (n)-built-up systems / p19 　3.2 Conditions on systems of fundamental sequences / p25 　3.3 Existence problems / p29 CHAPTER4 PROVABLY COMPUTABLE FUNCTIONS IN PEANO ARITHMETIC / p34 　4.1 Provable computability / p34 　4.2 Undecidable combinatorial statements / p40 　4.3 Relativized hierarchies / p44 CHAPTER5 THE FAST AND SLOW GROWING HIERARCHIES AND INDUCTIVE DEFINITIONS / p50 　5.1 Fast-growing versus slow-growing / p50 　5.2 The collapsing theorem and (3)-built-upness / p55 　5.3 Provable computability / p61 CHAPTER6 DISCUSSIONS / p69 　6.1 Undecidable statements in theories of arithmetic / p69 　6.2 Applications of subrecursive hierarchies / p71 ACKNOWLEDGMENTS / p75 REFERENCES / p76