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Summary: Predicative Categories of Classes
Michael Alton Warren
October 28, 2004
Contents
Abstract iii
Acknowledgments iv
Introduction v
1 #Pretopoi and Constructive Set Theories 1
1.1 #Pretopoi and Dependent Type Theory . . . . . . . . . . . . 1
1.1.1 #Pretopoi . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Dependent Type Theory . . . . . . . . . . . . . . . . . 2
1.1.3 Soundness and Completeness . . . . . . . . . . . . . . 4
1.2 Constructive Set Theories . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Notation and Axioms . . . . . . . . . . . . . . . . . . 6
1.2.2 Basic Properties . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 The Category of Sets . . . . . . . . . . . . . . . . . . . 12
1.2.4 Axioms of Infinity . . . . . . . . . . . . . . . . . . . . 14
2 Predicative Categories of Classes 16
2.1 Categories with Class Structure . . . . . . . . . . . . . . . . . 16
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