5.1 Introduction to metamathematics of HST 

    5.1a Internal core embeddings and interpretability 
    5.1b Metamathematics of HST: an overview
    
5.2 From internal to elementary external sets

    5.2a Interpretation of EEST in BST 
    5.2b Elementary external sets in external theories 
    5.2c Some basic theorems of EEST  
    5.2d Standard size, natural numbers, finiteness in EEST
     
5.3 Assembling of external sets in HST

    5.3a Well-founded trees 
    5.3b Coding of the assembling construction 
    5.3c Examples of codes 
    5.3d Regular codes
    
5.4 From elementary external to all external sets

    5.4a The domain of the interpretation 
    5.4b Basic relations between codes 
    5.4c The structure of basic relations 
    5.4d The interpretation and the embedding 
    5.4e Verification of the HST axioms 
    5.4f Superposition of interpretations 
    5.4g The problem of external sets revisited
    
5.5 The class L[I]: sets constructible from internal sets

    5.5a Sets constructible from internal sets 
    5.5b Proof of the theorem on I-constructible sets 
    5.5c The axiom of I-constructibility 
    5.5d Transfinite constructions in L[I]
    
Historical and other notes to Chapter 5