MST set theory is a set theory I created more as a joke to be the strongest axiomatic set theory, and it certainly achieved its goal! Since it isn't a true set theory, and was made more of a joke, I probably won't turn this into an actual Wikipedia article :)

Axioms

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This theory has a LOT of (27) axioms! Here is a complete list:

  1. Axiom of extensionality:  
  2. Axiom of regularity:  
  3. Axiom schema of specification:   is a formula in MST with all free variables among  ,  , ...,   (  is not free in  ). Then:  
  4. Axiom of pairing:  
  5. Axiom of union:  .
  6. Axiom schema of replacement:   is a formula in MST with all free variables among  ,  ,  ,  , ...,   (  is not free in  ). Then:  , where   is uniqueness quantification.
  7. Axiom of infinity:  
  8. Axiom of powerset:  
  9. Well-ordering theorem:  
  10. Axiom of induction:  
  11. Axiom of empty set:  
  12. Axiom schema of Σ0-separation: For a set   and Σ0-formula  ,  .
  13. Axiom schema of Σ1-separation: For a set   and Σ1-formula  ,  .
  14. Axiom schema of Σ0-collection: For a set   and Σ0-formula  ,   and  .
  15. Axiom schema of Σ1-collection: For a set   and Σ1-formula  ,   and  .
  16.  
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  26. Full second-order induction schema: For all second-order arithmetic and   formulas φ(n) with a free variable n and possible other free number or set variables (written m and X),  .
  27. Comprehension axiom schema: For all  ,  ,   and arithmetical formulas φ(n) with a free variable n and possibly other free variables, but not the variable Z,