In his paper "Undecidability without arithmetization," Andrzej Grzegorczyk introduces a theory of concatenation . We show that pairing is not definable in . We determine a reasonable extension of that is sequential, that is, has a good sequence coding.
"Growing Commas. A Study of Sequentiality and Concatenation." Notre Dame J. Formal Logic 50 (1) 61 - 85, 2009. https://doi.org/10.1215/00294527-2008-028