2013/03/18 by Randriambololona, Serge
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Logic (math.LO) #Primary 03C64 #Secondary 32B20
paper · doi:10.48550/arxiv.1303.4407
This article presents two constructions motivated by a conjecture of L. van den Dries and C. Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.