We take a magical tour in algebraic logic and its most novel applications.In algebraic logic we start from classical results on neat embeddingsdue to Andre′ka, Henkin, N′emeti, Monk and Tarski, all the wayto 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 generalrelativity and hypercomputation, this article aspires to present topics ofbroad interest in a way that is hopefully accessible to a large audience.Other topics deallt with include the interaction of algebraic and modallogic, the so–called (central still active) finitizability problem, G¨odels’sincompleteness Theorem in guarded fragments, counting the number ofsubvarieties of RCAω which is reminiscent of Shelah’s stability theoryand the interaction of algebraic logic and descriptive set theory as meansto approach Vaught’s conjecture in model theory. The interconectionsbetween algebraic geometry and cylindric algebra theory is surveyed andelaborated upon as a Sheaf theoretc duality. This article is not purelyexpository; far from it. It contains new results and new approaches toold paradigms. Furthermore, various scattered results in the literatureare presented from a holistic perspective highlighting similarities betweenseemingly remote areas in the literature. For example topoi andcategory theory are approached as means to unify apparently scatteredresults in the literature.
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