  Arbitrary Arrow Update Logic with Common Knowledge (AAULC) is a dynamic
epistemic logic with (i) an arrow update operator, which represents a
particular type of information change and (ii) an arbitrary arrow update
operator, which quantifies over arrow updates.
  By encoding the execution of a Turing machine in AAULC, we show that neither
the valid formulas nor the satisfiable formulas of AAULC are recursively
enumerable. In particular, it follows that AAULC does not have a recursive
axiomatization.
