Algebraic logic and topoi; a philosophical holistic approach

Tarek Sayed Ahmed
2020 International Journal of Algebra  
We take a magical tour in algebraic logic and its most novel applications. In algebraic logic we start from classical results on neat embeddings due to Andreḱa, Henkin, Németi, Monk and Tarski, all the way to recent results in algebraic logic using so-called rainbow constructions. Highlighting the connections with graph theory, model theory, finite combinatorics, and in the last decade with the theory of general relativity and hypercomputation, this article aspires to present topics of broad
more » ... erest in a way that is hopefully accessible to a large audience. Other topics deallt with include the interaction of algebraic and modal logic, the so-called (central still active) finitizability problem, Gödels's incompleteness Theorem in guarded fragments, counting the number of subvarieties of RCA ω which is reminiscent of Shelah's stability theory and the interaction of algebraic logic and descriptive set theory as means to approach Vaught's conjecture in model theory. The interconections between algebraic geometry and cylindric algebra theory is surveyed and elaborated upon as a Sheaf theoretc duality. This article is not purely expository; far from it. It contains new results and new approaches to old paradigms. Furthermore, various scattered results in the literature are presented from a holistic perspective highlighting similarities between seemingly remote areas in the literature. For example topoi and category theory are approached as means to unify apparently scattered results in the literature.
doi:10.12988/ija.2020.91249 fatcat:razdk5433fba5hrg6p6wb65a4y