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Preservativity logic: An analogue of interpretability logic for constructive theories
Author(s) -
Iemhoff Rosalie
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310023
Subject(s) - mathematics , intuitionistic logic , interpretability , multimodal logic , modal logic , dynamic logic (digital electronics) , intermediate logic , algebra over a field , constructive , class (philosophy) , property (philosophy) , modal , pure mathematics , discrete mathematics , artificial intelligence , computer science , propositional calculus , epistemology , description logic , process (computing) , programming language , philosophy , chemistry , physics , transistor , voltage , quantum mechanics , polymer chemistry
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.