THE AMBIGUOUS TYPE THEORY IS HEREDITARILY UNDECIDABLE
Andrey A. Kuzichev · Mathematical logic quarterly · 1992
Abstract The ambiguous type theory ATT is introduced in [1] in order to obtain a new proof of Specker's theorem on typical ambiguity [3]. In the present paper we imbed the recursively undecidable theory TR of a single transitive‐reflexive relation in an arbitrary stratified theory T such that T ⫅ ATT and so reduce the problem of derivability in TR to the same problem for T. From this it follows that ATT is hereditarily undecidable, i.e. ATT has no decidable subtheories.