A Model‐Theoretic Property of Sharply Bounded Formulae, with some Applications
Jan Johannsen · Mathematical logic quarterly · 1998
Abstract We define a property of substructures of models of arithmetic, that of being length‐initial, and show that sharply bounded formulae are absolute between a model and its length‐initial submodels. We use this to prove independence results for some weak fragments of bounded arithmetic by constructing appropriate models as length‐initial submodels of some given model.