Search
Now showing items 1-8 of 8
Article
Fragments of Arithmetic and true sentences
(Wiley, 2005)
By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the ¦n+1–sentences true in the standard model is the only (up to deductive equivalence) consistent ¦n+1–theory which extends the scheme of induction ...
Article
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 ...
Article
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 ...
Article
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 ...
Article
On the quantifier complexity of Δ n+1 (T)– induction
(Springer, 2004)
In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class ...
Article
A Note on Σ₁-Maximal Models
(Association for Symbolic Logic, 2007)
Let T be a recursive theory in the language of first order Arithmetic. We prove that if T extends: (a) the scheme of parameter free Δ₁-minimization (plus exp), or (b) the scheme of parameter free Π₁-induction, then there ...
Article
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 ...
Article
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 ...