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    An Introduction to Logic Algebras by Kramer, Nick

    We utilize the setting of Universal Algebra to introduce a new class of objects called logics, with the aim of generalizing the structure of familiar binary logic to a family of finite and countably infinite multi-valued logics. In Section 2, we explore several concepts and results parallel to those of more familiar algebraic structures and provide as an example an independent proof of the first isomorphism theorem for logics. In Section 3, we review some basic notions from Category Theory, which give us another lens through which to view logics, then prove several categorical results about them. In Section 4 we discuss implications of the idea of logics for various areas of mathematics, for the sake of brevity providing only a skeletal outline of what these might be, and in the last section we discuss the implications of logics on formal languages and natural deduction, providing a framework through which one might create generalized propositional logic.

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