Cobham has observed that Raphael Robinson's well known essentially undecidable theory
R remains essentially undecidable if the fifth axiom scheme
( x \leqq [`(n)] Ú[`(n)] \leqq x )\left( {x \leqq \bar n \vee \bar n \leqq x} \right)
is omitted. We note that whether the resulting system is in a sense

minimal essentially undecidable

depends on what the basic constants are taken to be. We give an essentially undecidable theory based on three axiom schemes involving only multiplication and less than or equals.