A Universal Algebra for the Variable-Free Fragment of \({\mathrm {RC}^\nabla }\)

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10703)


The language of Reflection Calculus \(\mathrm {RC}\) consists of implications between formulas built up from propositional variables and the constant ‘true’ using only conjunction and the diamond modalities which are interpreted in Peano arithmetic as restricted uniform reflection principles. In [6] we introduced \({\mathrm {RC}^\nabla }\), an extension of \(\mathrm {RC}\) by a series of modalities representing the operators associating with a given arithmetical theory T its fragment axiomatized by all theorems of T of arithmetical complexity \(\varPi ^0_n\), for all \(n>0\). In this paper we continue the study of the variable-free fragment of \({\mathrm {RC}^\nabla }\) and characterize its Lindenbaum–Tarski algebra in several natural ways.


Strictly positive logics Reflection principle Provability GLP 


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Authors and Affiliations

  1. 1.Steklov Mathematical Institute of the Russian Academy of SciencesMoscowRussia

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