Abstract

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 Presburger arithmetic with finite comprehension for bounded formulas). 0 Introduction. In the last two decades the research on bounded arithmetic has been focussed mainly on the theories of I \Delta 0 and I \Delta 0+\Omega 1 and on their fragments. The interest in these theories is in part motivated by complexity theoretical considerations. It is well known that the provably recursive function of I \Delta 0+\Omega 1 are those computable by algorithms in the polynomial time hierarchy while the provably recursive functions of I \Delta 0 correspond to the linear time hierarchy. Some open problems in bounded arithmetic are known to be equivalent to problems of complexity theory. More precisely, to the s...

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