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 class contains the canonical orthomodular frame of the logic and therefore characterises orthomodular quantum logic. To prove soundness, a further restriction is placed on admissible valuations which requires that they be point-generated in addition to the requirement that they return stable sets.
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DOI 10.1080/11663081.2016.1174361
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References found in this work BETA

Semantic Analysis of Orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
Models and Ultraproducts: An Introduction.J. L. Bell & A. B. Slomson - 1972 - Journal of Symbolic Logic 37 (4):763-764.
Orthomodularity is Not Elementary.Robert Goldblatt - 1984 - Journal of Symbolic Logic 49 (2):401-404.

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