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Article

Chajda, Ivan
Sheffer operation in ortholattices. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 44 (2005), issue 1, pp. 19-23
MSC: 06C15, 06E30 | MR 2218564 | Zbl 1091.06007
Keywords:
ortholattice; orthocomplementation; lattice with antitone involution; Sheffer operation
Summary:
We introduce the concept of Sheffer operation in ortholattices and, more generally, in lattices with antitone involution. By using this, all the fundamental operations of an ortholattice or a lattice with antitone involution are term functions built up from the Sheffer operation. We list axioms characterizing the Sheffer operation in these lattices.
References:
[1] Birkhoff G.: Lattice Theory. : Proc. Amer. Math. Soc., Providence, R. I. third edition, 1967. MR 0227053
[2] Grätzer G.: General Lattice Theory. : Birkhäuser Verlag, Basel. second edition, 1998. MR 1670580
[3] Sheffer H. M.: A set of five independent postulates for Boolean algebras. Trans. Amer. Math. Soc. 14 (1913), 481–488. MR 1500960
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