Mengenlehre
Set theory introduces the hypothetical existence of various "hyper-infinity" notions such as large cardinals. In 1989, it was proved that one such notion, axiom formula_25, implies the existence of an algebraic structure called an acyclic shelf which in turn implies the decidability of the word problem for the left self-distributivity law formula_26 a property that is a priori unconnected with large cardinals.