Refinements of provability and consistency principles for the second incompleteness theorem
Abstract
This paper continues the author's previous study Kura20, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of the present paper, we show that the set \E,C, D3\ suffices to establish the unprovability of the consistency statement \, PrT( 0=1 ). We also prove that the set \EU, CB∃\ yields formalized 1-completeness.
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