3.1 Introduction to internal set theories 

    3.1a Internal set theory 
    3.1b Bounded set theory 
    3.1c Internal sets interpret BST in the external universe 
    3.1d Basic internal set theory 
    3.1e Standard natural numbers and standard finite sets 
    3.1f Remarks on Basic Idealization and Saturation  
    
3.2 Development of bounded set theory 

    3.2a Half-bounded forms of Idealization 
    3.2b Reduction to two ``external'' quantifiers 
    3.2c Finite axiomatizability of BST and other corollaries 
    3.2d Collection in BST 
    3.2e Other basic theorems of BST 
    3.2f Introduction to the problem of external sets 
    3.2g More on ``external sets'' in BST 
    
3.3 Internal theories with partial  Saturation 
  
    3.3a Two schemes of partially saturated internal theories 
    3.3b \kappa-deep Basic Idealization scheme 
    3.3c \kappa-size Basic Idealization scheme 
    
3.4 Development of Nelson's internal set theory

    3.4a Bounded sets in IST 
    3.4b Bounded formulas: reduction to two ``external'' quantifiers 
    3.4c Collection in IST 
    3.4d Uniqueness in IST 
    
3.5 Truth definition in internal set theory 

    3.5a Truth definition for the standard universe 
    3.5b Connection with the ordinary truth
    3.5c Extension of the definition of formal truth
    
3.6 Second edition of IST

    3.6a Standard and nonstandard theories of Nelson's system 
    3.6b The background nonstandard universe 
    3.6c Three ``myths'' of IST
    
Historical and other notes to Chapter 3