Наредни састанак Семинара биће одржан у петак, 16. маја 2025. године, у сали 301ф Математичког института САНУ са почетком у 14.15.
Предавач: Меланија Митровић, Машински факултет Универзитет у Нишу
Наслов предавања: CONSTRUCTIVE RELATIONAL BINARY STRUCTURES WITH APARTNESS: BASICS AND POTENTIAL APPLICATIONS
Апстракт: It is only recently, due to the work of Melanija Mitrović and co-authors, that constructive mathematics has paid attention to semigroup theory. The use of intuitionistic logic in constructive mathematics facilitates the extraction of computational content from constructive proofs, something almost impossible within classical mathematics. M. Mitrović and co-authors`s approach to constructivism closely follows the paradigm of E. Bishop, whose informal system BISH, is developed in his seminal book Foundations of Constructive Analysis published in 1967. Inspired by results obtained from the use of interactive theorem-provers and the general theory of formal verification of constructive proofs, a new constructive algebraic theory, the so-called theory of semigroups with apartness was developed by M. Mitrović and co-authors: M. A. Baroni, S. Crvenković, E. Darpo, M. N. Hounkonnou, D. A. Romano, S. Silvestrov. In this talk, we will first briefly present some of the results obtained within the theory of sets with apartness and an appropriate constructive order theory we develop for sets with apartness as well as their applications to the class of constructive semigroups with apartness. Then we will present some of the main results on its proper subclass of constructive inverse semigroups with apartness, an important example of co-ordered semigroups with apartness. Although this talk will be mostly based on existing material, it is, by no means, an attempt to give complete overview of our existing results to the date.
Напомена: Предавање је могуће пратити на даљину путем линка
https://miteam.mi.sanu.ac.rs/asset/WbsehnSL4ZeTPJo6r
