Abstract

This is a reprinting of Ken Pledger’s PhD thesis, submitted to the University of Warsaw in 1980 with the degree awarded in 1981. It develops a one-sorted approach to the theory of plane geometry, based on the idea that the usually two-sorted theory “can be made one-sorted by keeping careful account of whether the incidence relation is iterated an even or odd number of times”.The one-sorted structures can also serve as Kripke frames for modal logics, and the thesis defines and studies two such logics that are validated by projective planes and elliptic planes respectively. It raises questions of logical completeness for these systems that are addressed in the first article of this journal issue.