Preservativity logic: An analogue of interpretability logic for constructive theories: An analogue of interpretability logic for constructive theories

Mathematical Logic Quarterly 49 (3):230 (2003)
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Abstract

In this paper we study the modal behavior of Σ‐preservativity, an extension of provability which is equivalent to interpretability for classical superarithmetical theories. We explain the connection between the principles of this logic and some well‐known properties of HA, like the disjunction property and its admissible rules. We show that the intuitionistic modal logic given by the preservativity principles of HA known so far, is complete with respect to a certain class of frames.

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10.1002/malq.200310023

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Rosalie Iemhoff
Utrecht University

Citations of this work

Proof theory for admissible rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.
On Geometric Implications.Amirhossein Akbar Tabatabai - forthcoming - Studia Logica:1-30.

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References found in this work

Rules and Arithmetics.Albert Visser - 1999 - Notre Dame Journal of Formal Logic 40 (1):116-140.

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