Displaying similar documents to “Lattices in ℤ² and the congruence xy+uv ≡ c(mod m)”

Distributive lattices have the intersection property

Henri Mühle (2021)

Mathematica Bohemica

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Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite distributive lattices in terms of the core...

Cyclic congruences of slim semimodular lattices and non-finite axiomatizability of some finite structures

Gábor Czédli (2022)

Archivum Mathematicum

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We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among finite graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the counterpart of this fact for all bipartite graphs in the class of all graphs is a well-known consequence of the compactness theorem.) Also, to exemplify that our method is applicable in various fields of mathematics, we prove that neither finite simple groups,...