Set Theory and Logic

   

Confirmation of the Collapse of the Buss Hierarchy of Bounded Arithmetics

Authors: Colin James III

Two seminal rules of inference evaluated as not tautologous. This means the following are also refuted: Buss’s hierarchy of bounded arithmetics does not entirely collapse; Takeuti’s argument implies P ≠ NP; and systems PV and PV−. What follows is that separation of bounded arithmetic using a consistency statement is not viable. Therefore the above are non tautologous fragments of the universal logic VŁ4.

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[v1] 2019-04-16 17:41:49

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