Constructive set theory

<p>Axiomatic constructive set theory is an approach to <a href="/facts/Constructivism_(mathematics)/1VtNuLwT">mathematical constructivism</a> following the program of <a href="/facts/Axiomatic_set_theory/1ptfsvUP">axiomatic set theory</a>.
The same <a href="/facts/First-order_logic/lcISqWIg">first-order</a> language with "
  
    
      
        =
      
    
    {\displaystyle =}
  
" and "
  
    
      
        ∈
      
    
    {\displaystyle \in }
  
" of classical set theory is usually used, so this is not to be confused with a <a href="/facts/Constructive_type_theory/qwkrpKlP">constructive types</a> approach.
On the other hand, some constructive theories are indeed motivated by their interpretability in <a href="/facts/Type_theory/xj0xzVqI">type theories</a>.
</p><p>In addition to rejecting the <a href="/facts/Principle_of_excluded_middle/tDhbugCN">principle of excluded middle</a> (
  
    
      
        
          
            P
            E
            M
          
        
      
    
    {\displaystyle {\mathrm {PEM} }}
  
), constructive set theories often require some logical quantifiers in their axioms to be set <a href="/facts/Bounded_quantifier/Q0Y7aTkG">bounded</a>. The latter is motivated by results tied to <a href="/facts/Impredicativity/gDuxRrb5">impredicativity</a>.
</p>

Constructive set theory open-in-new

Constructive set theory