This document presents conditions for when a tuple of operators is syndetically hypercyclic. It defines key terms like hypercyclic tuples, the hypercyclicity criterion, and syndetically hypercyclic. It proves that a tuple satisfies the hypercyclicity criterion if and only if for any syndetic sequences, the sequence of operators is hypercyclic. It also proves that a tuple is weakly mixing if and only if for any pair of open sets and syndetic sequences, there exist indices such that the operator tuple maps one set into the other. The document provides background, definitions, theorems, and references related to hypercyclic and syndetically hypercyclic tuples of operators.