Summary: Notes on Constructive Set Theory
DRAFT
Peter Aczel
Manchester
May 20, 1997
Contents
1 Introduction 1­1
2 Some Axiom Systems 2­1
2.1 Classical Set Theory . . . . . . . . . . . . . . . . . . . . . . . 2­1
2.2 Intuitionistic Set Theory . . . . . . . . . . . . . . . . . . . . . 2­2
2.3 Constructive Set Theory . . . . . . . . . . . . . . . . . . . . . 2­2
2.3.1 CZF 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 2­2
2.3.2 Constructive Zermelo Fraenkel, CZF . . . . . . . . . . 2­3
2.3.3 Basic Constructive Set Theory, BCST . . . . . . . . . 2­3
3 Elementary Mathematics in Constructive Set Theory 3­1
3.1 Class Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 3­1
3.2 Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3­2
3.2.1 Ordered Pairs . . . . . . . . . . . . . . . . . . . . . . . 3­2
3.2.2 Cartesian Products of Classes . . . . . . . . . . . . . . 3­2
3.2.3 Relations and Functions between Classes . . . . . . . . 3­3

Source: Aczel, Peter - Departments of Mathematics & Computer Science, University of Manchester

Collections: Mathematics