سمت در پژوهشگاه

پژوهشگر مقیم، پژوهشکده ریاضیات (1388 تا اکنون )

سمت‌های پیشین در پژوهشگاه

رئیس، پژوهشکده ریاضیات (1388 تا 1401) معاونت رئیس، پژوهشکده ریاضیات (1385 تا 1387) پژوهشگر وابسته، پژوهشکده ریاضیات (1385 تا 1386) پژوهشگر وابسته (غیرمقیم)، پژوهشکده ریاضیات (1384 تا 1384) پژوهشگر وابسته، پژوهشکده ریاضیات (1384 تا 1385) پژوهشگر وابسته، پژوهشکده ریاضیات (1383 تا 1384) پسا دکتری، پژوهشکده ریاضیات (1379 تا 1380)

علایق پژوهشی

Mathematical Logic, Model Theory, Application of Model Theory on Mathematical Structures

فعالیت‌های پژوهشی

This research programme deals essentially with finding new examples of simple theories using generic structure. It will also investigate general model theoretic properties os such structures and their applications in the classification of analytical structures. First, regarding the connection of generic structures to simple theories, this project will tackle the problem of finding some generalisations for the Independence Theorem Diagrams (ITD). This will lay sufficient ground for finding generic structures which have first order simple theories. Second, this project will seek to find a counterexample for the Stable Forking Conjecture. This will enable us to find a unprecedented simple theories whoes forking geometries are different from those of stable ones. Third, this project intends to probe the quality of the Lascar Strong types with Strong types under any generalisation of the ITD. This will justify the use of non-eliminable hyperimaginary elements, thus providing richer examples of simple theories. Fourth, this project will investigate the logical complexity of the full first order theory of {C>0,<=*}-generic theory and its simplicity. This research programme will also apply generic structures to some mathematical structures. First, using generic structures and stability concepts, we intend to study model theoretic properties of field of complex number with exponentiation. Second, this project shall explore the specific analytic O-minimal expansions of the field of real number using generic structures. This work will enable us to make progress towards understanding model theoretic properties of these analytic structures (using stability method) whose subtle connections with generic structures were first identified by Zilber.

پروژهٔ پژوهشی فعلی در پژوهشگاه

Simple Generic Structures

مقالات

1.	M. Pourmahdian (Joint with A. Valizadeh) Pseudofiniteness in Hrushovski Constructions Notre Dame J. Formal Logic 61 (2020), 1-10  [abstract]

2.	Z. Ghadrenezhad and M. Pourmahdian (Joint with H. Khalilian) Automorphism groups of generic structures: extreme amenability and amenability Fund. Math. (Accepted) [abstract]

3.	M. Pourmahdian and N. Roshandel Tavana (Joint with S. M. A. Khatami) From rational Godel logic to ultrametric logic J. Logic Comput. (Accepted) [abstract]

4.	M. Pourmahdian and N. R. Tavana (Joint with F. Didehvar) Effective metric model theory Math. Structures Comput. Sci. (2014), DOI: 10.1017/S0960129513000352  [abstract]

5.	M. Pourmahdian and N. R. Tavana Compactness in first-order Godel logics J. Logic Comput. (2012), DOI 10.1093/logcom/exs037  [abstract]

6.	M. Pourmahidan and M. Ali-Akbari Computational models of certain hyperspace of quasi-metric spaces LMCS 7 (2011), 1-25  [abstract]

7.	S. M. Bagheri and M. Pourmahdian Omitting types in an intermediate logic Studia Logica 97 (2011), 319-328  [abstract]

8.	M. Pourmahdian (Joint with M. Khani) On the metrizability of cone metric spaces Topology Appl. 158 (2011), 190-193  [abstract]

9.	M. Pourmahdian (Joint with M. Aliakbari) Completeness of hyperspaces of compact subsets of quasi-metric spaces Acta Math. Hungar. 127 (2010), 260-272  [abstract]

10.	M. Pourmahdian (Joint with F. Didehvar and K. Ghasemloo) Effectiveness in RPL, with applications to continuous logic Ann. Pure Appl. Logic 161 (2010), 709-828  [abstract]

11.	M. Pourmahdian (Joint with M. Ali-Akbari and B. Honari) Any T1 space has a continous poset model Topology Appl. (Accepted) [abstract]

12.	M. Pourmahdian (Joint with M. Ali-Akbari, B. Honari, and M. M. Rezaeii) The space of formal balls and models of quasi-metric spaces Math. Structures Comput. Sci. (Accepted) [abstract]

13.	S. M. Bagheri and M. Pourmahdian Elementary amalgamation and joint embedding property for intermediate logics Log. J. IGPL (Accepted) [abstract]

14.	S. M. Bagheri and M. Pourmahdian Diagram construction in intuitionistic logic Log. J. IGPL 16 (2006), 889-901  [abstract]

15.	M. Pourmahdian (Joint with F. Wagner) A simple positive Robinson theory with LSTP ≠ STP Lect. Notes Log. 26 (2006), 270-283  [abstract]

16.	M. Pourmahdian The stable forking conjecture in homogeneous model theory Log. J. IGPL 12 (2004), 171-180  [abstract]

17.	M. Pourmahdian Simple generic structures Ann. Pure Appl. Logic 121 (2003), 227-260  [abstract]

18.	M. Pourmahdian The stable forking conjecture and generic structures Arch. Math. Logic 42 (2003), 415-421  [abstract]

19.	M. Pourmahdian Smooth classes without AC and Robinson theories J. Symbolic Logic 67 (2002), 1274-1294  [abstract]

20.	S.S. Goncharov and M. Pourmahdian Iterated expansions of models for countable theories and their applications Algebra and Logic 34 (1995), 346-358  [abstract]

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