XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 05/01/2026 17:04, Mike Terry wrote:   
      
   > There is a related phenomenon which is much more severe, which we have   
   >    ⊢ p(1)   
   >    ⊢ p(2)   
   >    ⊢ p(3)   
   >    ...   
   > and additionally   
   >    ⊢ ¬∀n p(n)   
   >   
   > This is called ω-inconsistency.   
      
   Does the ω in ω-inconsistency refer to the number larger than all   
   naturals? It seems an obvious focus of the matter for the fixed-point of   
   the successor function and perhaps sufficient that one gave its name to   
   the other.   
      
   And so does ω properly refer to the fixed-point of the successor function?   
      
      
   --   
   Tristan Wibberley   
      
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