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Artículo
On the Optimality of Conservation Results for Local Reflection in Arithmetic
(Association for Symbolic Logic, 2013)
Let T be a recursively enumerable theory extending Elementary Arithmetic EA. L. D. Beklemishev proved that the Σ2 local reflection principle for T, (T), is conservative over the Σ1 local reflection principle, (T), with ...
Artículo
On axiom schemes for T-provably Δ1 formulas
(Springer, 2014)
This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are Δ1 provably in an arithmetic theory T. In ...
Artículo
A note on parameter free Π1-induction and restricted exponentiation
(Wiley, 2011)
We characterize the sets of all Π2 and all $\mathcal {B}(\Sigma _{1})$equation image (= Boolean combinations of Σ1) theorems of IΠ−1 in terms of restricted exponentiation, and use these characterizations to prove that both ...