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Algebraic Set Theory Steve Awodey
 

Summary: Notes on
Algebraic Set Theory
Steve Awodey
Haute-Bodeux, June 2005
Contents
1 Introduction 2
2 Categories of classes 7
2.1 Small maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Powerclasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Universes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Class categories . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 The topos of sets . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 The set theory BIST 13
3.1 Class soundness of BIST . . . . . . . . . . . . . . . . . . . . . 14
3.2 Class completeness of BIST . . . . . . . . . . . . . . . . . . . 14
4 Ideal completion of a topos 16
4.1 Small maps in sheaves . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Powerclasses and universes in ideals . . . . . . . . . . . . . . . 19
4.3 Topos models of BIST . . . . . . . . . . . . . . . . . . . . . . 21
5 Ideal representation of class categories 23

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics