On End‐Extensions of Models of ¬exp
Fernando A.F. Ferreira · Mathematical logic quarterly · 1996
Abstract Every model of IΔ0is the tally part of a model of the stringlanguage theory Th‐FO (a main feature of which consists in having induction on notation restricted to certainAC0. sets). We show how to “smoothly” introduce in Th‐FO the binary length function, whereby it is possible to make exponential assumptions in models of Th‐FO. These considerations entail that every model of IΔ0+ ¬exp is a proper initial segment of a model of Th‐FO and that amodicumof bounded collection is true in these models. Mathematics Subject Classification: 03F30, 03C62, 68Q15.