English

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

Logic 2023-07-11 v3

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.

Keywords

Cite

@article{arxiv.2207.02709,
  title  = {A parametrised axiomatization for a large number of restricted second-order logics},
  author = {Guillermo Badia and John Lane Bell},
  journal= {arXiv preprint arXiv:2207.02709},
  year   = {2023}
}