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/