Archive for Mathematical Logic 46 (5-6):489-516 (2007)

Abstract
We define a theory of two-sort bounded arithmetic whose provably total functions are exactly those in ${\mathcal{F}_{LOGCFL}}$ by way of a generalized quantifier that expresses computations of SAC 1 circuits. The proof depends on Kolokolova’s conditions for the connection between the provable capture in two-sort theories and descriptive complexity
Keywords Mathematics   Algebra   Mathematics, general   Mathematical Logic and Foundations
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DOI 10.1007/s00153-007-0052-4
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Notes on Polynomially Bounded Arithmetic.Domenico Zambella - 1996 - Journal of Symbolic Logic 61 (3):942-966.

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