We define a recursive theory which axiomatizes a class of models of IΔ₀ + Ω ₃ + ¬ exp all of which share two features: firstly, the set of Δ₀ definable elements of the model is majorized by the set of elements definable by Δ₀ formulae of fixed complexity; secondly, Σ₁ truth about the model is recursively reducible to the set of true Σ₁ formulae of fixed complexity.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-2-2,
author = {Zofia Adamowicz and Leszek Aleksander Ko\l odziejczyk and Pawe\l\ Zbierski},
title = {An application of a reflection principle},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {139-159},
zbl = {1053.03032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-2-2}
}
Zofia Adamowicz; Leszek Aleksander Kołodziejczyk; Paweł Zbierski. An application of a reflection principle. Fundamenta Mathematicae, Tome 177 (2003) pp. 139-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-2-2/