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THE
${\text{\Sigma }}_1 $-PROVABILITY LOGIC OF
$HA^{\text{*}} $
Published online by Cambridge University Press: 12 July 2019
Abstract
For the Heyting Arithmetic HA, $HA^{\text{*}} $ is defined [14, 15] as the theory
$\left\{ {A|HA \vdash A^\square } \right\}$, where
$A^\square $ is called the box translation of A (Definition 2.4). We characterize the
${\text{\Sigma }}_1 $-provability logic of
$HA^{\text{*}} $ as a modal theory
$iH_\sigma ^{\text{*}} $ (Definition 3.17).
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- Copyright © The Association for Symbolic Logic 2019
References
REFERENCES
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