The decidability of a class of AE sentence in the isols
Erik Ellentuck, Alfred B. Manaster · Pacific Journal of Mathematics · 1972
The isols are a recursive analogue of the Dedekind finite cardinals originally developed by Dekker.In this paper a metatheorem is proved which shows that for certain sentences J>/ about addition in which no existential quantifier precedes a universal quantifier, the truth of *S%f in the natural numbers is sufficient to ensure the truth of Stf in the isols.A more general class of sentences is also considered and it is seen that the applicability of the metatheorem is also necessary for the truth of any sentence in this class.It follows that there exists a decision procedure for that class of sentences.Extensions of these results to the case of the cosimple isols are also considered.