Abstract Necessitism, Contingentism, and Theory Equivalence is a dissertation on issues in higher-order modal metaphysics. Consider language with identity which the universal quantifier interpreted as expressing (unrestricted) quantification necessity operator metaphysical necessity. The main question addressed concerns correct theory formulated this language. A different that also takes centre...

We show that the category of diagrams of topological spaces (or simplicial sets) admits many interesting model category structures in the sense of Quillen [8]. The strongest one renders any diagram of simplicial complexes and simplicial maps between them both fibrant and cofibrant. Namely, homotopy invertible maps between such are the weak equivalences and they are detectable by the "spaces of ...

We prove a version of Koszul duality and the induced derived equivalence for Adams connected A∞-algebras that generalizes the classical Beilinson-Ginzburg-Soergel Koszul duality. As an immediate consequence, we give a version of the Bernšte˘ ın-Gel'fand-Gel'fand correspondence for Adams connected A∞-algebras. We give various applications. For example, a connected graded algebra A is Artin-Schel...

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This paper discusses strong shift equivalence and counterexamples to the long standing Shift Equivalence Problem in symbolic dynamics. We also discuss how strong shift equivalence theory is closely related to areas of mathematics outside dynamics such as algebraic K-theory, cyclic homology, and topological quantum field theory.