Grant GX20-31529X
1.1.2020 - 31.12.2024
Grantor: Czech Science Foundation
Abstract convergence schemes and their complexities
Objectives:
Abstract convergence schemes are basic category-theoretic structures which serve as universes for studying infinite evolution-like processes and their limiting behavior. Convergence schemes endowed with extra structures provide an applicable framework for studying both discrete and continuous processes as well as their random variants.
The main goal of the project is unifying and extending several concepts from model theory, algebra, topology and analysis, related to generic structures. We propose studying selected topics within the framework of abstract convergence schemes, addressing questions on their complexity and classification. One of our inspirations is the theory of universal homogeneous models, where convergence of finite structures is involved. Another motivation is set-theoretic forcing, where a convergence scheme is simply a partially ordered set of approximations of some ``unreachable" objects, living outside of the universe of set theory.
Main investigator:
IM team members:
Participating institutions:
Institute of Mathematics, Czech Academy of Sciences
