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  1. The de Jongh property for Basic Arithmetic.Mohammad Ardeshir & S. Mojtaba Mojtahedi - 2014 - Archive for Mathematical Logic 53 (7-8):881-895.
    We prove that Basic Arithmetic, BA, has the de Jongh property, i.e., for any propositional formula A built up of atoms p1,..., pn, BPC⊢\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\vdash}$$\end{document}A if and only if for all arithmetical sentences B1,..., Bn, BA⊢\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\vdash}$$\end{document}A. The technique used in our proof can easily be applied to some known extensions of BA.
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  • The Σ1-provability logic of HA.Mohammad Ardeshir & Mojtaba Mojtahedi - 2018 - Annals of Pure and Applied Logic 169 (10):997-1043.
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  • The first-order logic of CZF is intuitionistic first-order logic.Robert Passmann - 2024 - Journal of Symbolic Logic 89 (1):308-330.
    We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine the resulting notion of realisability with Beth semantics. On the way, we also show that the propositional admissible rules of CZF are exactly those of intuitionistic propositional logic.
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  • Logics of intuitionistic Kripke-Platek set theory.Rosalie Iemhoff & Robert Passmann - 2021 - Annals of Pure and Applied Logic 172 (10):103014.
    We investigate the logical structure of intuitionistic Kripke-Platek set theory , and show that the first-order logic of is intuitionistic first-order logic IQC.
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  • Decidability of admissibility: On a problem by Friedman and its solution by Rybakov.Jeroen P. Goudsmit - 2021 - Bulletin of Symbolic Logic 27 (1):1-38.
    Rybakov proved that the admissible rules of $\mathsf {IPC}$ are decidable. We give a proof of the same theorem, using the same core idea, but couched in the many notions that have been developed in the mean time. In particular, we illustrate how the argument can be interpreted as using refinements of the notions of exactness and extendibility.
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