The Σ₁ Provability Logic of HA

2014/09/19 by Ardeshir, Mohammad, Mojtahedi, S. Mojtaba
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1409.5699

Abstract

In this paper we introduce a modal theory H_σ, which is sound and complete for arithmetical Σ₁ substitutions in \bf HA, in other words, we will show that H_σ is the Σ₁-provability logic of \bf HA. Moreover we will show that H_σ is decidable. As a by-product of these results, we show that \bf HA + \Box\bot has de Jongh property.

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