We consider the notion of bounded $m$-ary patch-width defined in , 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.
"Relational structures constructible by quantifier free definable operations." J. Symbolic Logic 72 (4) 1283 - 1298, December 2007. https://doi.org/10.2178/jsl/1203350786