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We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general modeltheoretical investigations on fragments of bounded arithmetic.
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We show that every model of I-\Delta_0 has an end extension to a model of a theory (extending Buss' S^0_2) where logspace computable function are formalizable. We also show the existence of an isomorphism between models of I-\Delta_0 and models of linear arithmetic LA (i.e., secondorder Presb...
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The axioms for "independent choices" presented in van Lambalgen [1992] are strengthened here, so that they can be seen as introducing a new type of indiscernibles in set theory. The resulting system allows for the construction of natural inner models. The article is organised as follows. Secti...