The logic of arithmetical hierarchy

Annals of Pure and Applied Logic 66 (2):89-112 (1994)
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Abstract

Formulas of the propositional modal language with the unary modal operators □, Σ1, 1, Σ2, 2,… are considered as schemata of sentences of arithmetic , where □A is interpreted as “A is PA-provable”, ΣnA as “A is PA-equivalent to a Σn-sentence” and nA as “A is PA-equivalent to a Boolean combination of Σn-sentences”. We give an axiomatization and show decidability of the sets of the modal formulas which are schemata of: PA-provable, true arithmetical sentences

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Citations of this work

Modal Matters for Interpretability Logics.Evan Goris & Joost Joosten - 2008 - Logic Journal of the IGPL 16 (4):371-412.
Self provers and Σ1 sentences.Evan Goris & Joost Joosten - 2012 - Logic Journal of the IGPL 20 (1):1-21.
Interpolation and the Interpretability Logic of PA.Evan Goris - 2006 - Notre Dame Journal of Formal Logic 47 (2):179-195.

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References found in this work

A course on bimodal provability logic.Albert Visser - 1995 - Annals of Pure and Applied Logic 73 (1):109-142.
Sentences implying their own provability.David Guaspari - 1983 - Journal of Symbolic Logic 48 (3):777-789.

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