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Artículo
Existentially Closed Models and Conservation Results in Bounded Arithmetic
(Oxford Academic, 2009)
We develop model-theoretic techniques to obtain conservation results for first order Bounded Arithmetic theories, based on a hierarchical version of the well-known notion of an existentially closed model. We focus on the ...
Artículo
Local induction and provably total computable functions
(Elsevier, 2014)
Let I¦− 2 denote the fragment of Peano Arithmetic obtained by restricting the induction scheme to parameter free ¦2 formulas. Answering a question of R. Kaye, L. Beklemishev showed that the provably total computable ...
Artículo
Envelopes, indicators and conservativeness
(Wiley, 2006)
A well known theorem proved (independently) by J. Paris and H. Friedman states that BΣn +1 (the fragment of Arithmetic given by the collection scheme restricted to Σn +1‐formulas) is a Πn +2‐conservative extension of IΣn ...