On the provability logic of bounded arithmetic

Annals of Pure and Applied Logic 61 (1-2):75-93 (1991)
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Abstract

Let PLω be the provability logic of IΔ0 + ω1. We prove some containments of the form L ⊆ PLω < Th(C) where L is the provability logic of PA and Th(C) is a suitable class of Kripke frames

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