Relational structures constructible by quantifier free definable operations

Abstract

We consider the notion of bounded $m$-ary patch-width defined in [9], and its very close relative $m$-constructibility defined below. We show that the notions of $m$-constructibility all coincide for $m \geq$ 3, while 1-constructibility is a weaker notion. The same holds for bounded $m$-ary patch-width. The case $m =$ 2 is left open.