• دکتری (1376)

    ریاضی محض - منطق ریاضی

    لیون، فرانسه

  • کارشناسی‌ارشد (1371)

    ریاضی محض

    دانشگاه صنعتی شریف،

  • کارشناسی (1369)

    ریاضی محض

    دانشگاه صنعتی شریف،

  • منطق ریاضی
  • نظریه مدل ها

    اینجانب دوره کارشناسی و کارشناسی ارشد را در دانشگاه صنعتی شریف در رشته ریاضی محض گذراندم (1371-1365). دوره دکتری را در دانشگاه لیون فرانسه بودم و در گرایش منطق ریاضی کار کردم (1376-1373). از 76 تا خرداد 79 در دانشگاه اصفهان تدریس کردم و از 79 تا کنون در دانشگاه تربیت مدرس مشغول به کار می باشم. با پژوهشگاه دانشهای بنیادی نیز همکاری داشتم.



    The logic of linear propositions

    Seyed-Mohammad Bagheri
    Journal PapersLogic Journal of the IGPL , 2019 March 21, {Pages }


    I prove linear compactness and linear completeness for various forms of linear propositional logic where the value space is a module over a ring.

    The isomorphism theorem for linear fragments of continuous logic

    Seyed-Mohammad Bagheri
    Journal PapersarXiv preprint arXiv:1910.00776 , 2019 October 2, {Pages }


    The ultraproduct construction is generalized to -ultramean constructions () by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments of continuous logic. A powermean variant of Keisler-Shelah isomorphism theorem is proved for . It is then proved that -sentences (and their approximations) are exactly those sentences of continuous logic which are preserved by such constructions. Some other applications are also given.

    Continuous integration logic

    Seyed-Mohammad Bagheri, Massoud Pourmahdian
    Journal PapersarXiv preprint arXiv:1910.00191 , 2019 October 1, {Pages }


    We combine continuous and integral logics and found a logical framework for metric measure spaces equipped with a family of continuous relations and operations. We prove the ultraproduct theorem and deduce compactness and other usual results. We also give applications of the compactness theorem in metric measure theory.Subjects: Logic (math. LO)Cite as: arXiv: 1910.00191 [math. LO](or arXiv: 1910.00191 v1 [math. LO] for this version)Submission historyFrom: Seyed-Mohammad Bagheri [view email][v1] Tue, 1 Oct 2019 03: 59: 20 UTC (16 KB)

    Maximality of linear continuous logic

    Mahya Malekghasemi, Seyed‐Mohammad Bagheri
    Journal PapersMathematical Logic Quarterly , Volume 64 , Issue 3, 2018 July , {Pages 185-191 }


    The linear compactness theorem is a variant of the compactness theorem holding for linear formulas. We show that the linear fragment of continuous logic is maximal with respect to the linear compactness theorem and the linear elementary chain property. We also characterize linear formulas as those preserved by the ultramean construction.

    Categoricity and quantifier elimination for intuitionistic theories

    Seyed Mohammad Bagheri
    Journal PapersLogic in Tehran , Volume 26 , 2017 March 30, {Pages 23-41 }


    We study a class of Kripke models with a naturally and well-behaved embedding relation. After proving a completeness theorem, we generalize some usual classical theorems of model theory into this framework. As an application, we give examples of non-classical ω-categorical theories which admit quantifier elimination.

    Completeness for linear continuous logic

    Seyed-Mohammad Bagheri, Roghieh Safari
    Journal PapersJournal of Logic and Computation , Volume 27 , Issue 4, 2015 September 30, {Pages 985-998 }


    We prove completeness of linear continuous logic introduced in and with respect to a linear system of axioms and rules.

    Eberlein-Smulian compactness and Kolmogorov extension theorems; a model theoretic approach

    Seyed-Mohammad Bagheri, Karim Khanaki
    Journal PapersarXiv preprint arXiv:1509.03193 , 2015 September , {Pages }


    This paper has two parts. First, we complete the proof of the Kolmogorov extension theorem for unbounded random variables using compactness theorem of integral logic which was proved for bounded case in [8]. Second, we give a proof of the Eberlein-Smulian compactness theorem by Ramsey's theorem and point out the correspondence between this theorem and a result in Shelah's classification theory.

    On the ultramean construction

    Roghieh Safari, Seyed-Mohammad Bagheri
    Journal PapersIranian Journal of Mathematical Sciences and Informatics , Volume 9 , Issue 2, 2014 January 1, {Pages 109-119 }


    We use the ultramean construction to prove linear compactness theorem. We also extend the Rudin-Keisler ordering to maximal probability charges and characterize it by embeddings of power ultrameans..

    Linear model theory for Lipschitz structures

    Seyed-Mohammad Bagheri
    Journal PapersArchive for Mathematical Logic , Volume 53 , Issue 08-Jul, 2014 November 1, {Pages 897-927 }


    I study definability and types in the linear fragment of continuous logic. Linear variants of several definability theorems such as Beth, Svenonus and Herbrand are proved. At the end, a partial study of the theories of probability algebras, probability algebras with an aperiodic automorphism and AL-spaces is given.

    Preservation theorems in linear continuous logic

    Seyed‐Mohammad Bagheri, Roghieh Safari
    Journal PapersMathematical Logic Quarterly , Volume 60 , Issue 3, 2014 May , {Pages 168-176 }


    Linear continuous logic is the fragment of continuous logic obtained by restricting connectives to addition and scalar multiplications. Most results in the full continuous logic have a counterpart in this fragment. In particular a linear form of the compactness theorem holds. We prove this variant and use it to deduce some basic preservation theorems.

    A proof of completeness for linear continuous logic

    Roghieh Safari, SM Bagheri
    Journal Papers , 2014 March , {Pages }


    A (linear) condition is an expression of the form ϕ⩽ ψ where ϕ, ψ are linear formulas. If ϕ, ψ are sentences, it is called a closed condition. The notion M⊨(ϕ⩽ ψ)(a) is defined in the obvious way. A collection of closed conditions is called a linear theory. M is a model of T, denoted M⊨ T, if M satisfies every condition in T.

    Preservation theorems in {L} ukasiewicz\model theory

    Seyed-Mohammad Bagheri, Morteza Moniri
    Journal PapersIranian Journal of Fuzzy Systems , Volume 10 , Issue 3, 2013 June 1, {Pages 103-113 }


    We present some model theoretic results for Lukasiewicz predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the Lukasiewicz BL-algebra. We also prove some appropriate preservation theorems concerning universal and inductive theories. Finally, Skolemization and Morleyization in this framework are discussed and some natural examples of fuzzy theories are presented.

    Preservation theorems in Lukasiewicz Model Theory

    SM BAGHERI, M Moniri
    Journal Papers , , {Pages }


    Quantified universes and ultraproducts

    Alireza Mofidi, Seyed‐Mohammad Bagheri
    Journal PapersMathematical Logic Quarterly , Volume 58 , Issue 1‐2, 2012 February , {Pages 63-74 }


    A quantified universe is a set M equipped with a Riesz space article amssymb empty A_n of real functions on Mn, for each n, and a second order operation article amssymb empty I:A→\mathbbR. Metric structures 4, graded probability structures 9 and many other structures in analysis are examples of such universes. We define ultraproduct of quantified universes and study properties preserved by this construction. We then discuss logics defined on the basis of classes of quantified universes which are closed under this construction.

    Random variables and integral logic

    Karim Khanaki, Seyed‐Mohammad Bagheri
    Journal PapersMathematical Logic Quarterly , Volume 57 , Issue 5, 2011 October , {Pages 494-503 }


    We study model theory of random variables using finitary integral logic. We prove definability of some probability concepts such as having F(u) as distribution function, independence and martingale property. We then deduce Kolmogorov's existence theorem from the compactness theorem.

    Omitting Types in an Intermediate Logic

    Seyed-Mohammad Bagheri, Massoud Pourmahdian
    Journal PapersStudia Logica , Volume 97 , Issue 3, 2011 April 1, {Pages 319-328 }


    We prove an omitting types theorem and one direction of the related Ryll-Nardzewski theorem for semi-classical theories introduced in [2].

    A Łoś type theorem for linear metric formulas

    Seyed‐Mohammad Bagheri
    Journal PapersMathematical Logic Quarterly , Volume 56 , Issue 1, 2010 January , {Pages 78-84 }


    We define an ultraproduct of metric structures based on a maximal probability charge and prove a variant of Łoś theorem for linear metric formulas. We also consider iterated ultraproducts (? 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

    An arithmetical view to first-order logic

    Seyed Mohammad Bagheri, Bruno Poizat, Massoud Pourmahdian
    Journal PapersAnnals of Pure and Applied Logic , Volume 161 , Issue 6, 2010 March 1, {Pages 745-755 }


    A value space is a topological algebra B equipped with a non-empty family of continuous quantifiers: B∗→ B. We will describe first-order logic on the basis of B. Operations of B are used as connectives and its relations are used to define statements. We prove under some normality conditions on the value space that any theory in the new setting can be represented by a classical first-order theory.

    The Proceedings of the IPM 2007 Logic Conference

    K Aehlig, A Beckmann, M Ardeshir, R Ramezanian, SM Bagheri, B Poizat, M Pourmahdian, LD Beklemishev, S Barry Cooper, F Didehvar, K Ghasemloo, J Landes, JB Paris, A Vencovsk?, J V??n?nen, W Hodges
    Journal Papers , 2010 January , {Pages }


    Page 1. Annals of Pure and Applied Logic 161 (2010) iv Contents lists available at ScienceDirect Annals of Pure and Applied Logic journal homepage: www.elsevier.com/locate/apal Contents Special Issue The Proceedings of the IPM 2007 Logic Conference A. Enayat and I. Kalantari Preface 709 K. Aehlig and A. Beckmann On the computational complexity of cut-reduction 711 M. Ardeshir and R. Ramezanian The double negation of the intermediate value theorem 737 SM Bagheri, B. Poizat and M. Pourmahdian An arithmetical view to first-order logic 745 LD Beklemishev Kripke semantics for provability logic GLP 756 S. Barry Cooper Extending and interpreting Post's programme 775 F. Didehvar, K. Ghasemloo and M. Pourmahdian Effectiveness in RPL, with applicatio

    The logic of integration

    Seyed-Mohammad Bagheri, Massoud Pourmahdian
    Journal PapersArchive for Mathematical Logic , Volume 48 , Issue 5, 2009 June 1, {Pages 465-492 }


    We develop a model theoretic framework for studying algebraic structures equipped with a measure. The real line is used as a value space and its usual arithmetical operations as connectives. Integration is used as a quantifier. We extend some basic results of pure model theory to this context and characterize measurable sets in terms of zero-sets of formulas.

    دروس نیمسال جاری

    • كارشناسي ارشد
      نظريه مدل 1 ( واحد)
      دانشکده علوم ریاضی، گروه رياضي محض

    دروس نیمسال قبل

    • كارشناسي ارشد
      جبر پيشرفته ( واحد)
      دانشکده علوم ریاضی، گروه رياضي محض
    • دكتري
      نظريه مجموعه ها ( واحد)
      داده ای یافت نشد
      داده ای یافت نشد



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