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MAM Seminars Autumn term 2017

Higher seminars in the subject Mathematics/Applied Mathematics, Autumn term 2017. 
School of Education, Culture and Communication (UKK), Mälardalen University.

October 25, 2017, Wednesday, 15.30-16.30

Speaker: Melanija  Mitrović, University of Niš, Serbia

Title: Semilattices of Archimedean Semigroups


The Stockholm Logic Seminar

Organisers: Erik Palmgren (chair), Peter LeFanu Lumsdaine, Per Martin-Löf (emeritus)

November 15, 10.00–11.45

Speaker: Melanija  Mitrović, University of Niš, Serbia

Title: An introduction to a development of the theory of constructive semigroups with apartness

http://logic.math.su.se/seminar/

ALGEBRA AND GEOMETRY SEMINAR
Department of Mathematics, Uppsala University
Usually: Tuesday's 15.15-17.00 in 64119

 

December 12, 2017,  Tuesday, 15.15-17.00

Speaker: Melanija  Mitrović, University of Niš, Serbia

Title:  Constructive semigroups with apartness - a new approach to semigroup   theory

The theory of constructive semigroups with apartness are a new approach  to semigroup theory, and not a new class of  semigroups. Of course, our work is partly inspired by classical semigroup theory, but, on the other hand, it is distinguished from it by two significiant aspects: first, we use  intuitionistic logic rather than classical, secondly, our work is based on the notion of apartness (between elements, elements and sets). In short, framework of our work is constructive mathematics -  roughly, mathematics with intuitionistics logic. Constructive mathematics is not unique notion. Principle trends include the following varieties: INT, RUSS, BISH.  Constructive mathematics in our work (and in this talk) is Errett Bishop - style constructive mathematics,  BISH, [2].  Despite the fact that constructive algebra is (relatively) old discipline (developed among others by L. Kronecker, van der Waerden, A. Heyting), it is,  compared with constructive analysis and topology, still of modest size.  Following  [1], the principal novelty in treating  basic algebraic structures constructively is that apartness  becomes a fundamental notion, i.e. one axiomatizes rings, groups, and fields with apartness.  The main aim of our work within constructive semigroups with apartness  (was, is, and) will be  to give a little progress in that direction. Although the lecture will be  based on material given in [4,5], it is, by no means an attempt to give a complete overview of our existing results. Important  sourse of ideas and notions of our work is [3]. An example of application(s) of these ideas can be found in [6]. The standard reference for constructive algebra is [7].

References:

1.   
M. J. Beeson:  Foundations of Constructive Mathematics, Springer-Verlag, 1985.
2.   
E. Bishop: Foundations of Constructive Analysis, McGraw-Hill, New York, 1967.
3.   
D. S. Bridges, L. S. Vita:  Apartness and Uniformity - A Constructive Development, CiE series on Theory and Applications of Computability, Springer, 2011.
4.   
S. Crvenković,  M. Mitrović,  D. A. Romano:  Semigroups with Apartness, Mathematical Logic Quarterly,   59 (6), 2013, 407-414.
5.   
S. Crvenković,  M. Mitrović,  D. A. Romano:  Basic Notions of (Constructive) Semigroups with Apartness, Semigroup  Forum, June 2016, Volume 92, Issue 3, 659-674.
6.   
H. Geuvers, R. Pollack, F. Wiedijk, J. Zwanenburg:  A Constructive Algebraic Hierarchy in Coq,  J. Symbolic Computation (2002) 34, 271-286.
7.
R. Mines, F. Richman, W. Ruitenburg:  A Course of Constructive Algebra, Springer-Verlag, New York,  1988.

http://www2.math.uu.se/~mazor/seminar.html




                                                                                         Chairs of the Seminar:

                                                                                         Douglas S. Bridges
                                                                                         Melanija Mitrović




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