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Mathematics > Logic

arXiv:1804.09451 (math)
[Submitted on 25 Apr 2018 (v1), last revised 5 Jun 2018 (this version, v2)]

Title:Provability Logic and the Completeness Principle

Authors:Albert Visser, Jetze Zoethout
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Abstract:In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\Box$ and $\triangle$ that prove the schemes $A\to\triangle A$ and $\Box\triangle S\to\Box S$ for $S\in\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\Sigma_1$-provability logic of Heyting Arithmetic.
Subjects: Logic (math.LO)
MSC classes: 03F45, 03F50, 03F55
Cite as: arXiv:1804.09451 [math.LO]
  (or arXiv:1804.09451v2 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1804.09451

Submission history

From: Albert Visser [view email]
[v1] Wed, 25 Apr 2018 09:42:52 UTC (35 KB)
[v2] Tue, 5 Jun 2018 07:20:24 UTC (34 KB)
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