Annals of Pure and Applied Logic 162 (12):981-990 (2011)

Abstract
The theory , axiomatized by the induction scheme for sharply bounded formulae in Buss’ original language of bounded arithmetic , has recently been unconditionally separated from full bounded arithmetic S2. The method used to prove the separation is reminiscent of those known from the study of open induction.We make the connection to open induction explicit, showing that models of can be built using a “nonstandard variant” of Wilkie’s well-known technique for building models of IOpen. This makes it possible to transfer many results and methods from open to sharply bounded induction with relative ease.We provide two applications: the Shepherdson model of IOpen can be embedded into a model of , which immediately implies some independence results for ; extended by an axiom which roughly states that every number has a least 1 bit in its binary notation, while significantly stronger than plain , does not prove the infinity of primes
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DOI 10.1016/j.apal.2011.06.003
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References found in this work BETA

The Strength of Sharply Bounded Induction.Emil Jeřábek - 2006 - Mathematical Logic Quarterly 52 (6):613-624.
Multifunction Algebras and the Provability of PH↓.Chris Pollett - 2000 - Annals of Pure and Applied Logic 104 (1-3):279-303.
Bootstrapping, Part I.Sedki Boughattas & J. -P. Ressayre - 2010 - Annals of Pure and Applied Logic 161 (4):511-533.

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Citations of this work BETA

Open Induction in a Bounded Arithmetic for TC0.Emil Jeřábek - 2015 - Archive for Mathematical Logic 54 (3-4):359-394.

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