8.1 Nonstandard set theory of Kawa"i 

    8.1a The axioms of Kawa"i 's theory 
    8.1b Metamathematical properties 
    8.1c Special model axiom
    
8.2 ``Nonstandard set theory'' of Hrbacek

    8.2a Axioms 
    8.2b Additional axioms of Collection    
    8.2c Conservativity and consistency 
    8.2d Remarks and exercises
    
8.3 Non-well-found -ed set theories

    8.3a Boffa's non-well-founded set theory
    8.3b Extensions of proper classes 
    8.3c Applications to nonstandard analysis 
    8.3d Alpha theory
    8.3e Interpretation of Alpha theory in ZFBC
    
8.4 Miscellanea: some other theories 

    8.4a A theory with ``definable'' Saturation     
    8.4b Stratified nonstandard set theories 
    8.4c Nonstandard class theories
    
Historical and other notes to Chapter 8