For a large class of Hardy fields their extensions containing non--germs are constructed. Hardy fields composed of only non--germs, apart from constants, are also considered.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-8,
author = {Krzysztof Grelowski},
title = {Extending Hardy fields by non-$^{$\infty$}$-germs},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {281-297},
zbl = {1147.26018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-8}
}
Krzysztof Grelowski. Extending Hardy fields by non-$^{∞}$-germs. Annales Polonici Mathematici, Tome 93 (2008) pp. 281-297. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-3-8/