An application of a reflection principle
Volume 180 / 2003
Fundamenta Mathematicae 180 (2003), 139-159
MSC: Primary 03F30.
DOI: 10.4064/fm180-2-2
Abstract
We define a recursive theory which axiomatizes a class of models of $I\Delta _0 + \Omega _3 + \neg \mathop {\rm exp}\nolimits $ all of which share two features: firstly, the set of $\Delta _0$ definable elements of the model is majorized by the set of elements definable by $\Delta _0$ formulae of fixed complexity; secondly, $\Sigma _1$ truth about the model is recursively reducible to the set of true $\Sigma _1$ formulae of fixed complexity.
