XPost: sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   "standard model"   
     I saw one hushnow thing on stackoverflow about this, everything else   
   was about quantum physics where "standard" is used in its natural sense   
   of a well known and understood point in a space against which we can   
   reference deviations.   
      
   "predicate"   
     This has a meaning in formal systems as something that joins objects   
   of a system to form a statement of the system.   
     Do you mean to use "propositional function" or, by "truth predicate"   
   do you mean to refer to the former sense in an example such as '⊢' which   
   joins one object to nothing else to form a statement that asserts the   
   object?   
      
   A sensibly weak PA is found with semantics in (I think all of) Haskell,   
   Idris, Agda2, Epigram2 via Algebraic Data Types. There are   
   nonprogramming systems such as System F that contain it along with very   
   much more besides.   
      
      
   Topic formed with reference to:   
      
   On 17/01/2026 21:08, olcott wrote:   
   > For nearly a century, discussions of arithmetic have quietly   
   > relied on a fundamental conflation: the idea that   
   > “true in arithmetic” meant “true in the standard model of ℕ.”   
   > But PA itself has no truth predicate, no internal semantics,   
   > and no mechanism for assigning truth values. So what was   
   > called “true in arithmetic” was always meta-theoretic truth   
   > about arithmetic, imported from an external model and never   
   > grounded inside PA.   
   >   
   > This conflation was rarely acknowledged, and it shaped the   
   > interpretation of Gödel’s incompleteness theorems, independence   
   > results like Goodstein and Paris–Harrington, and the entire   
   > discourse around “true but unprovable” statements.   
   >   
   > My work begins by correcting this foundational error.   
   >   
   > PA has no internal truth predicate, so classical claims of   
   > “true in arithmetic” were always meta-theoretic   
      
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