First-order frames for orthomodular quantum logic

Abstract

One of the main problems of the orthoframe approach to quantum logic was that orthomodularity could not be captured by any first-order condition. This paper studies an elementary and natural class of orthomodular frames that can work around this limitation. Set-theoretically, the frames we propose form a natural subclass of the orthoframes , where is an irreflexive and symmetric relation on X. More specifically, they are partially-ordered orthoframes with a designated subset . Our frame...