metamathematics
noun
                                                                                                                            
                                                            meta·math·e·mat·ics
                    
                                                                                                              
                                                                                                                                  ˈme-tə-ˌmath-ˈma-tiks  
                                                                                                                              
            -ma-thə-
                                                      
                                                          
            
               plural in form but usually singular in construction             
        
    
                                
              
          
                                                      : a field of study concerned with the formal structure and properties (such as the consistency and completeness of axioms) of mathematical systems                                      
                
                    
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