Page 6 - Textos de Matemática Vol. 38
P. 6
iv Contents
Peter Koepke
Ordinals, Computations, and Models of Set Theory
1 Introduction.............................. 43
2 Ordinalnumbers ........................... 45
2.1 Definitions .......................... 45
2.2 Inductionandrecursion ................... 47
2.3 Ordinalarithmetic ...................... 48
2.4 TheGo¨delpairingfunction ................ 50
3 Registermachines .......................... 50
3.1 Unlimitedregistermachines-URMs . . . . . . . . . . . . 51 3.2 Algorithms .......................... 52
4 Ordinalcomputations ........................ 54 4.1 Ordinalregistermachines-ORMs . . . . . . . . . . . . . 54 4.2 Ordinalalgorithms...................... 56
5 ThetheorySOofsetsofordinals.................. 58
6 Assembling sets along wellfounded relations . . . . . . . . . . . . 61
7 TheclassofpointssatisfiesZFC .................. 63
8 Anordinalcomputabletruthpredicate . . . . . . . . . . . . . . . 69
8.1 3-adic representations and ordinal stacks . . . . . . . . . . 69
8.2 Stackrecursion........................ 70
8.3 Arecursivetruthpredicate ................. 73
9 Computingamodelofsettheory................ .. 74
9.1 Ordinal computability corresponds to constructibility .. 75 10 An application: the generalized continuum hypothesis in L . . .. 76 Bibliography ................................ 77
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