Abstract

We study a propositional polymodal provability logic GLP introduced
by G. Japaridze. The previous treatments of this logic, due to Japaridze
and Ignatiev (see [11, 7]), heavily relied on some non-finitary principles
such as transfinite induction up to ε0 or reflection principles. In fact, the
closed fragment of GLP gives rise to a natural
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