Well-orders in the transfinite Japaridze algebra

This article studies the transfinite propositional provability logics GLP(A) and their corresponding algebras. These logics have for each ordinal xi . We will focus on the closed fragment of GLP(Lambda) (i.e. where no propositional variables occur) and worms therein. Worms are iterated consistency expressions of the form ... inverted perpendicular. Beklemishev has defined well-orderings (xi epsilon On) for some worm A. One of these characterizations is in terms of a second kind of transfinite iteration called cohyperation.This article studies the transfinite propositional provability logics GLP(A) and their corresponding algebras. These logics have for each ordinal xi . We will focus on the closed fragment of GLP(Lambda) (i.e. where no propositional variables occur) and worms therein. Worms are iterated consistency expressions of the form ... inverted perpendicular. Beklemishev has defined well-orderings (xi epsilon On) for some worm A. One of these characterizations is in terms of a second kind of transfinite iteration called cohyperation.A