Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • adj. Describing a lattice that is both orthocomplemented and modular

Etymologies

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Examples

  • V with L (V) orthomodular, is necessarily complete.

    Puppet X: 1

  • Conversely, an orthocomplemented poset is orthomodular iff

    Puppet X: 1

  • The lemma tells us that every orthocoherent orthoalgebra is, inter alia, an orthomodular poset.

    Puppet X: 1

  • Let us call a complete orthomodular lattice satisfying the hypotheses of Piron's theorem a Piron lattice.

    Puppet X: 1

  • In other words, in such cases we have only one logic, which is a complete orthomodular lattice.

    Puppet X: 1

  • This is not generally an order-isomorphism, but when it is, we obtain a complete orthomodular lattice, and thus come a step closer to the projection lattice of a Hilbert space.

    Puppet X: 1

  • Mackey presents a sequence of six axioms, framing a very conservative generalized probability theory, that underwrite the construction of a ˜logic™ of experimental propositions, or, in his terminology, ˜questions™, having the structure of a sigma-orthomodular poset.

    Puppet X: 1

  • Thus, orthomodular posets (the framework for Mackey's version of quantum logic) are equivalent to orthocoherent orthoalgebras.

    Puppet X: 1

  • Let L be a complete, atomic, irreducible orthomodular lattice satisfying the atomic covering law.

    Puppet X: 1

  • Π will inherit from L the structure of a complete lattice, which will then automatically be orthomodular by Lemma 4.3.

    Puppet X: 1

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