Mengato, Stefano (2017) On Logical connectives and quantifiers as adjoint functors. [Magistrali biennali]
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This thesis deals with the issue of treating logical connectives, quantifiers and equality in categorical terms, by means of adjoint functors combined into the notion of hyperdoctrine, introduced by Francis William Lawvere in 1969. After proving the general Theorem of Soundness and Completeness for the intuitionistic predicate logic with equality with respect to hyperdoctrines, we formulate instances of such categorical models by using H-valued sets and Kleene realizability, in order to produce easily models and countermodels for logical formulas.
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