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The Field of Reals with Multisummable Series and the Exponential Function
Author(s) -
Dries Lou Van Den,
Speissegger Patrick
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012648
Subject(s) - mathematics , exponential function , series (stratigraphy) , field (mathematics) , double exponential function , natural exponential family , pure mathematics , discrete mathematics , mathematical analysis , paleontology , biology
We show that the field of real numbers with multisummable real power series is model complete, o‐minimal and polynomially bounded. Further expansion by the exponential function yields again a model complete and o‐minimal structure which is exponentially bounded, and in which the Gamma function on the positive real line is definable. 2000 Mathematics Subject Classification : primary 03C10, 32B05, 32B20; secondary, 26E05.