We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.
@article{urn:eudml:doc:44260,
title = {A failure of quantifier elimination.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {10},
year = {1997},
pages = {209-216},
zbl = {0879.03011},
mrnumber = {MR1485300},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44260}
}
Macintyre, Angus; Marker, David. A failure of quantifier elimination.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 209-216. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44260/