Notre Dame Journal of Formal Logic

Interpolation and the Interpretability Logic of PA

Evan Goris


In this paper we will be concerned with the interpretability logic of PA and in particular with the fact that this logic, which is denoted by ILM, does not have the interpolation property. An example for this fact seems to emerge from the fact that ILM cannot express Σ₁-ness. This suggests a way to extend the expressive power of interpretability logic, namely, by an additional operator for Σ₁-ness, which might give us a logic with the interpolation property. We will formulate this extension, give an axiomatization which is modally complete and arithmetically complete (although for proofs of these theorems we refer to an earlier paper), and investigate interpolation. We show that this logic still does not have the interpolation property.

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Notre Dame J. Formal Logic, Volume 47, Number 2 (2006), 179-195.

First available in Project Euclid: 25 July 2006

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
Secondary: 03F30: First-order arithmetic and fragments

provability logic interpretability logic interpolation


Goris, Evan. Interpolation and the Interpretability Logic of PA. Notre Dame J. Formal Logic 47 (2006), no. 2, 179--195. doi:10.1305/ndjfl/1153858645.

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