XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 05/01/2026 17:04, Mike Terry wrote:   
   > On 04/01/2026 22:13, Jeff Barnett wrote:   
      
   >> In a little larger system, perhaps with an   
   >> induction axiom, or a meta system it might be trivial to prove the   
   > whole thing with a   
   >> finite effort.   
   >   
   > Yes that's common.  For example there are common systems where for all   
                                                                        ^^^   
                                                                       each   
   > (natural numbers) m,n we can prove   
     ^^^^^^^^^^^^^^^^^^^^^   
     m,n constructible only such that they represent natural numbers?   
      
   >   
   >    ⊢  +  =  +    
   >   
   > typically using induction over m,n (in the meta-system).   
      
   Is it always the case that valid episystems derive production rules for   
   deductions for a system? Ie, a derivation in a meta-system generated by   
   applying an episystem to a system tells us how to generate a deduction   
   for the base-system?   
      
   It kind of looks that way to me so far and that I should expect nothing   
   more than that from them.   
      
      
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   Tristan Wibberley   
      
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