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Homomorphisms, quotient groups, isomorphism theorems.Prerequisite courses for Undegraduates: UM 203 Part A: Group theory M., A Course on Mathematical Logic, Universitext, Springer-Verlag, 2008. I., A Course in Mathematical Logic for Mathematicians, Second Edition, Graduate Texts in Mathematics, Springer-Verlag, 2010. Homotopy Type Theory: Univalent Foundations of Mathematics, Institute for Advanced Studies, Princeton 2013 available at.Connections with programming in functional languages will be explored. Most of the material will be developed using the dependently typed language Idris.Homotopy Type Theory: propositions as types, the identity type family, topological view of the identity type, foundations of homotopy type theory.First order logic: First order languages, deduction and truth, Models, Godel’s completeness and compactness theorems.Basic type theory: terms and types, function types, dependent types, inductive types.This course is an introduction to logic and foundations from both a modern point of view (based on type theory and its relations to topology) as well as in the traditional formulation based on first-order logic. It will be useful to have some familiarity with programming.Some background in algebra and topology will be assumed.Mendelsohn, First-order modal logic, Kluwer, 1998. Fitting, Proof methods for modal and intuitionistic logics, Reidel, 1983. Fitting, First-order logic and automated theorem proving, Springer, 2nd edition, 1996. Hodges, Mathematical logic, Oxford Univ Press, 2007. Intuitionistic logic: Kripke frames, tableaus, completeness.Tableaus, rigid and flexible designators, non-designating terms,ĭefinite descriptions, ontological arguments. First-order modal logics: Kripke frames with constant and varying domains,.
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Tableaus, completeness, finite model property, decision procedures Modal logics: Kripke frames, characterization of frame conditions,.Models, Smullyan-style tableaus, completeness and compactness theorems. First-order logic: First-order languages, deduction and truth,.Methods will be discussed, the emphasis will be on proofs using tableaus. Modern treatments of some non-classical logics. This course is an introduction to standard material in logic,īased on classical first-order logic, after which it ventures into Background in reading and doing mathematical proofs will be assumed.No prior knowledge of logic is assumed.MA 209: Logic: classical, modal and intuitionistic