We consider the predicative modal provability logic of Peano Arithmetic where the interpretation of each atomic modal formulas is required to be belong to the set of arithmetic formulas of complexity Sigma_0^n. We show that for distinct values of n the corresponding modal formulas form a strict hierarchy and each of them is complete for the class Pi^0_2.
Sigma_n Interpretations of modal logic
BERARDUCCI, ALESSANDRO
1989-01-01
Abstract
We consider the predicative modal provability logic of Peano Arithmetic where the interpretation of each atomic modal formulas is required to be belong to the set of arithmetic formulas of complexity Sigma_0^n. We show that for distinct values of n the corresponding modal formulas form a strict hierarchy and each of them is complete for the class Pi^0_2.File in questo prodotto:
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