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  1.  47
    Gentzen-Style Axiomatizations for Some Conservative Extensions of Basic Propositional Logic.Mojtaba Aghaei & Mohammad Ardeshir - 2001 - Studia Logica 68 (2):263-285.
    We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.
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  2.  15
    A Gentzen-Style Axiomatization for Basic Predicate Calculus.Mojtaba Aghaei & Mohammad Ardeshir - 2003 - Archive for Mathematical Logic 42 (3):245-259.
    We introduce a Gentzen-style sequent calculus axiomatization for Basic Predicate Calculus. Our new axiomatization is an improvement of the previous axiomatizations, in the sense that it has the subformula property. In this system the cut rule is eliminated.
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  3.  12
    Combinatorial Unprovability Proofs and Their Model-Theoretic Counterparts.Mojtaba Aghaei & Amir Khamseh - 2014 - Notre Dame Journal of Formal Logic 55 (2):231-244.
    For a function $f$ with domain $[X]^{n}$, where $X\subseteq\mathbb{N}$, we say that $H\subseteq X$ is canonical for $f$ if there is a $\upsilon\subseteq n$ such that for any $x_{0},\ldots,x_{n-1}$ and $y_{0},\ldots,y_{n-1}$ in $H$, $f=f$ iff $x_{i}=y_{i}$ for all $i\in\upsilon$. The canonical Ramsey theorem is the statement that for any $n\in\mathbb{N}$, if $f:[\mathbb{N}]^{n}\rightarrow\mathbb{N}$, then there is an infinite $H\subseteq\mathbb{N}$ canonical for $f$. This paper is concerned with a model-theoretic study of a finite version of the canonical Ramsey theorem with a largeness (...)
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  4.  10
    A Bounded Translation of Intuitionistic Propositional Logic Into Basic Propositional Logic.Mojtaba Aghaei & Mohammad Ardeshir - 2000 - Mathematical Logic Quarterly 46 (2):195-206.
    In this paper we prove a bounded translation of intuitionistic propositional logic into basic propositional logic. Our new theorem, compared with the translation theorem in [1], has the advantage that it gives an effective bound on the translation, depending on the complexity of formulas.
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