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On the “Problem of the Last Root” for Exponential Terms

✍ Scribed by Helmut Wolter

Publisher
John Wiley and Sons
Year
1985
Tongue
English
Weight
376 KB
Volume
31
Category
Article
ISSN
0044-3050

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✦ Synopsis

For our investigations of the last root, problem for exponential terms in T-models we need some results and definitions from [l], which we shortly summarize here.

Let C* be a fixed model of T, Gf a substructure of C* and C k OEF. Further, let C', be the set of functions in C* defined by means of terms from 2 with one variable and parameters from C. W'ith the aid of WILKIE'S results one can prove that for each E C' , there are element's a. 5 b in C' * such that f is defined for all x 2 a and f is constant or strongly monotonc for .2: 2 b. Especially, if f + 0. then /(.?:) is positive resp. ncgtttivc from onn point on. If f , g E C' , , then by fg iff f ( n ) = g(.r) for some a E C* and all .r 2 a , 11*

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