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  1.  10
    Decidability and Specker Sequences in Intuitionistic Mathematics.Mohammad Ardeshir & Rasoul Ramezanian - 2009 - Mathematical Logic Quarterly 55 (6):637-648.
    A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema about intuitionistic decidability that asserts “there exists an intuitionistic enumerable set that (...)
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  2.  90
    A Solution to the Surprise Exam Paradox in Constructive Mathematics.Mohammad Ardeshir & Rasoul Ramezanian - 2012 - Review of Symbolic Logic 5 (4):679-686.
    We represent the well-known surprise exam paradox in constructive and computable mathematics and offer solutions. One solution is based on Brouwer’s continuity principle in constructive mathematics, and the other involves type 2 Turing computability in classical mathematics. We also discuss the backward induction paradox for extensive form games in constructive logic.
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  3.  18
    The Double Negation of the Intermediate Value Theorem.Mohammad Ardeshir & Rasoul Ramezanian - 2010 - Annals of Pure and Applied Logic 161 (6):737-744.
    In the context of intuitionistic analysis, we consider the set consisting of all continuous functions from [0,1] to such that =0 and =1, and the set consisting of ’s in where there exists x[0,1] such that . It is well-known that there are weak counterexamples to the intermediate value theorem, and with Brouwer’s continuity principle we have . However, there exists no satisfying answer to . We try to answer to this question by reducing it to a schema about intuitionistic (...)
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  4.  17
    On the Constructive Notion of Closure Maps.Mohammad Ardeshir & Rasoul Ramezanian - 2012 - Mathematical Logic Quarterly 58 (4-5):348-355.
    Let A be a subset of the constructive real line. What are the necessary and sufficient conditions for the set A such that A is continuously separated from other reals, i.e., there exists a continuous function f with f−1 = A? In this paper, we study the notions of closed sets and closure maps in constructive reverse mathematics.
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    Everyone Knows That Everyone Knows.Rahim Ramezanian, Rasoul Ramezanian, Hans van Ditmarsch & Malvin Gattinger - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and Their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 117-133.
    A gossip protocolGossip protocol is a procedure for sharing secrets in a network. The basic action in a gossip protocolGossip protocol is a telephone call wherein the caller and the callee exchange all the secrets they know. An agent who knows all secrets is an expert. The usual termination condition is that all agents are experts. Instead, we explore some protocols wherein the termination condition is that all agents know that all agents are experts. We call such agents super experts. (...)
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