ABSTRACT
In more recent years,20 Turing’s result has been improved to the extent that all we need are sentences of the relatively simple form Vx 3y VzMxyz, where M contains no quantifiers. Hence, even the decision problem for the simple class of V3V sentences in the pre dicate calculus is unsolvable. Moreover, the method of proof also yields a procedure by which every sentence of the predicate calculus is correlated with one in the simple form. Hence, the class of V3V sentences forms a ‘reduction class.’ There are various other reduction classes.
