We extend first-order logic to include variadic function symbols and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
"The First-Order Syntax of Variadic Functions." Notre Dame J. Formal Logic 54 (1) 47 - 59, 2013. https://doi.org/10.1215/00294527-1731380