# Orthomodular Lattices

Elżbieta Mądra; Adam Grabowski

Formalized Mathematics (2008)

- Volume: 16, Issue: 3, page 277-282
- ISSN: 1426-2630

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topElżbieta Mądra, and Adam Grabowski. "Orthomodular Lattices." Formalized Mathematics 16.3 (2008): 277-282. <http://eudml.org/doc/267071>.

@article{ElżbietaMądra2008,

abstract = {The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings - as a relational structure (poset) and as a lattice.As a preliminary work, we present the proofs of the dependence of other axiomatizations of ortholattices. The formalization of the properties of orthomodular lattices follows [4].},

author = {Elżbieta Mądra, Adam Grabowski},

journal = {Formalized Mathematics},

language = {eng},

number = {3},

pages = {277-282},

title = {Orthomodular Lattices},

url = {http://eudml.org/doc/267071},

volume = {16},

year = {2008},

}

TY - JOUR

AU - Elżbieta Mądra

AU - Adam Grabowski

TI - Orthomodular Lattices

JO - Formalized Mathematics

PY - 2008

VL - 16

IS - 3

SP - 277

EP - 282

AB - The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings - as a relational structure (poset) and as a lattice.As a preliminary work, we present the proofs of the dependence of other axiomatizations of ortholattices. The formalization of the properties of orthomodular lattices follows [4].

LA - eng

UR - http://eudml.org/doc/267071

ER -

## References

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