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