Por Eduardo Magalhães (Universidade do Porto).

Since the development of o-minimality in the 1980s, the structure of definable groups within o-minimal structures has been extensively studied. A natural question is whether we can get similar structural insights for more general algebraic systems. In this talk, I’ll share the work I’ve been doing for my Master’s thesis over the past academic year, which focuses on definable semigroups in o-minimal structures. The central theme of the work is to explore the extent to which classical theorems can be adapted to this new context. Some of the results include definable versions of well-known theorems about compact semigroups, including the existence of idempotents in definably compact semigroups, as well as the presence of definable minimal left and right ideals, and definable kernels. I also introduce and explore definably compact definable paragroups, which arise as a natural generalization of definable groups.

Transmissão via Zoom (pw: 919 4789 5133).