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Статья

On provability logics with linearly ordered modalities

Studia Logica. 2014. Vol. 102. No. 3. P. 541-566.
Beklemishev L. D., Fernandez-Duque D., Joosten J. J.

We introduce the logics GLPΛ, a generalization of Japaridze’s polymodal provability logic GLPω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLPω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLPΛ and the decidability of GLPΛ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment ofGLPΛ.