Journal of the london mathematical society-second series vol:78 pages:198-212
We consider the ordered field which is the completion of the Puiseux series field over R equipped with a ring of analytic functions on [-1, 1](n) which contains the standard subanalytic functions as well as functions given by t-adically convergent power series, thus combining the analytic structures of Denef and van den Dries [Ann. of Math. 128 (1988) 79-138] and Lipshitz and Robinson [Bull. London Math. Soc. 38 (2006) 897-906]. We prove quantifier elimination and o-minimality in the corresponding language. We extend these constructions and results to rank n ordered fields R. (the maximal completions of iterated Puiseux series fields). We generalize the example of Hrushovski and Peterzil [J. Symbolic Logic 72 (2007) 119-122] of a sentence which is not true in any o-minimal expansion of R (shown in [Bull. London Math. Soc. 38 (2006) 897-906] to be true in an o-minimal expansion of the Puiseux series field) to a tower of examples of sentences a., true in R., but not true in any o-minimal expansion of any of the fields R,R1,...,Rn-1.