International Journal of Theoretical Physics

, Volume 31, Issue 5, pp 789–807

Filters and supports in orthoalgebras

  • D. J. Foulis
  • R. J. Greechie
  • G. T. Rüttimann
Article

DOI: 10.1007/BF00678545

Cite this article as:
Foulis, D.J., Greechie, R.J. & Rüttimann, G.T. Int J Theor Phys (1992) 31: 789. doi:10.1007/BF00678545

Abstract

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.

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • D. J. Foulis
    • 1
  • R. J. Greechie
    • 2
    • 3
  • G. T. Rüttimann
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherst
  2. 2.Department of MathematicsKansas State UniversityManhattan
  3. 3.Department of MathematicsLouisiana Technical UniversityRuston
  4. 4.Department of Mathematics and StatisticsUniversity of BerneBerneSwitzerland