XPost: comp.theory, sci.logic, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-11-20, dart200  wrote:   
   > a) you can construct halting paradoxes that contradicts multiple and   
   > possibly even infinite deciders. certainly any finite set, after which   
      
   This is not possible in general. The diagonal test case must make   
   exactly one decision and then behave in a contradictory way: halt or   
   not. If it interrogates as few as two deciders, it becomes intractable   
   if their decisions differ: to contradict one is to agree with the other.   
      
   If the deciders are H0(P) { return 0; } and H1(P) { return 1; } you can   
   see that between the two of them, they cover the entire space: there   
   cannot be a signal case whch both of these don't get right. One   
   correctly decides all nonterminating cases; the other correctly decies   
   all terminating cases, and every case is one or the other.   
      
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