Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics Describing a
lattice that is both orthocomplemented andmodular
Etymologies
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Examples

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

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

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

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

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

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

Conversely, an orthocomplemented poset is orthomodular iff

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

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

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 sigmaorthomodular poset.
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