  We define an ordinalized version of Kleene's realizability interpretation of
intuitionistic logic by replacing Turing machines with Koepke's ordinal Turing
machines (OTMs), thus obtaining a notion of realizability applying to arbitrary
statements in the language of set theory. We observe that every instance of the
axioms of intuitionistic first-order logic are OTM-realizable and consider the
question which axioms of Friedman's Intuitionistic Set Theory (IZF) and Aczel's
Constructive Set Theory (CZF) are OTM-realizable.
  This is an introductory note, and proofs are mostly only sketched or omitted
altogether. It will soon be replaced by a more elaborate version.
