Chain conditions in free products of lattices with infinitary operations
George Grätzer, András Sándor Hajnal, David Kelly · Pacific Journal of Mathematics · 1979
There are many facts known about the size of subsets of certain kinds in free lattices and free products of lattices.Examples: every chain in a free lattice is at most countable; every "large" subset contains an independent set; if the free product of a set of lattices contains a "long" chain, so does the free product of a finite subset of this set of lattices.Here we investigate these problems in the setting of a variety V of m-lattices, where m is an infinite regular cardinal.An m-lattice L is a lattice in which for any nonempty set S with |S|