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arXiv · 2207.02709

A parametrised axiomatization for a large number of restricted second-order logics

Guillermo Badia·John Lane Bell
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Abstract

By limiting the range of the predicate variables in a second-order language one may obtain restricted versions of second-order logic such as weak second-order logic or definable subset logic. In this note we provide an infinitary strongly complete axiomatization for several systems of this kind having the range of the predicate variables as a parameter. The completeness argument uses simple techniques from the theory of Boolean algebras.

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Guillermo Badia, John Lane Bell. 2022-07-06. A parametrised axiomatization for a large number of restricted second-order logics. https://arxiv.org/abs/2207.02709

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