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THE ${\text{\Sigma }}_1 $-PROVABILITY LOGIC OF $HA^{\text{*}} $

Published online by Cambridge University Press:  12 July 2019

MOHAMMAD ARDESHIR  and
MOJTABA MOJTAHEDI
MOHAMMAD ARDESHIR
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES SHARIF UNIVERSITY OF TECHNOLOGY TEHRAN, IRANE-mail: [email protected]
MOJTABA MOJTAHEDI
Affiliation:
DEPARTMENT OF MATHEMATICS STATISTICS AND COMPUTER SCIENCE COLLEGE OF SCIENCES, UNIVERSITY OF TEHRAN TEHRAN, IRANE-mail: [email protected]
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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).

Keywords

03F4503B4503F5003F55completeness principleHeyting arithmeticintuitionistic logicmodal logicprovability logic
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 3 , September 2019 , pp. 1118 - 1135
Copyright
Copyright © The Association for Symbolic Logic 2019 

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