
{\bf Generalized cardinal properties  of lattices and lattice ordered groups}

{\it J{\'a}n Jakub{\'\i}k}


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ABSTRACT:

We denote by $K$ the class of all cardinals; put $K'=K\cup\{
\infty\}$. Let $\Cal C$ be a class of algebraic systems. A
generalized cardinal property $f$ on $\Cal C$ is defined to
be a rule which assings to each $A\in\Cal C$ an element $fA$
of $K'$ such that, whenever $A_1, A_2\in\Cal C$ and
$A_1\simeq A_2$, then $fA_1=fA_2$. In this paper we are
interested mainly in the cases when (i) $\Cal C$ is the
class of all bounded lattices $B$ having more than one
element, or (ii) $\Cal C$ is a class of lattice ordered
groups.


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{\it AMS classification (1991): }
06F15, 06B06

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{\it Keywords: }
bounded lattice, lattice ordered group, generalized cardinal property, homogenity

