International Journal of Theoretical Physics

, Volume 31, Issue 5, pp 789-807

First online:

Filters and supports in orthoalgebras

  • D. J. FoulisAffiliated withDepartment of Mathematics and Statistics, University of Massachusetts
  • , R. J. GreechieAffiliated withDepartment of Mathematics, Kansas State UniversityDepartment of Mathematics, Louisiana Technical University
  • , G. T. RüttimannAffiliated withDepartment of Mathematics and Statistics, University of Berne

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An orthoalgebra, which is a natural generalization of an orthomodular lattice or poset, may be viewed as a “logic” or “proposition system” and, under a welldefined set of circumstances, its elements may be classified according to the Aristotelian modalities: necessary, impossible, possible, and contingent. The necessary propositions band together to form a local filter, that is, a set that intersects every Boolean subalgebra in a filter. In this paper, we give a coherent account of the basic theory of Orthoalgebras, define and study filters, local filters, and associated structures, and prove a version of the compactness theorem in classical algebraic logic.