We prove that every implicative aBE algebra satisfies the transitivity property. This means is a Tarski algebra, and thus also commutative BCK algebra.

In Zermelo-Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to “Every set has the same cardinal number as some transitive set.” In set theory without the axiom of choice, we study the deductive strength of this and similar statements introduced by von Rimscha. We shall use the standard notation and termi...

Recently, we have introduced six types of composition ternary fuzzy relations. These compositions are close in spirit to the binary Based on these composition, several transitivity a relation and investigated their basic properties. In this paper, prove additional properties characterizations relation. Also, provide representation theorem for relations satisfying transitivity. Finally, focus pr...