The real field with convergent generalized power series

Lou van den Dries; Patrick Speissegger

The real field with convergent generalized power series

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on [0,1] by a series ∑c_nx^αn with 0 ≤ α_n → ∞ and ∑ |c_n|r^αn < ∞ for some r > 1 is definable. This expansion is polynomially bounded.

Original language	English (US)
Pages (from-to)	4377-4421
Number of pages	45
Journal	Transactions of the American Mathematical Society
Volume	350
Issue number	11
State	Published - Dec 1 1998

Keywords

Blowing-up
Model completeness
O-minimal structures
Power series

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Cite this

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title = "The real field with convergent generalized power series",

abstract = "We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on [0,1] by a series ∑cnxαn with 0 ≤ αn → ∞ and ∑ |cn|rαn < ∞ for some r > 1 is definable. This expansion is polynomially bounded.",

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author = "{van den Dries}, Lou and Patrick Speissegger",

year = "1998",

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AU - van den Dries, Lou

AU - Speissegger, Patrick

PY - 1998/12/1

Y1 - 1998/12/1

N2 - We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on [0,1] by a series ∑cnxαn with 0 ≤ αn → ∞ and ∑ |cn|rαn < ∞ for some r > 1 is definable. This expansion is polynomially bounded.

AB - We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on [0,1] by a series ∑cnxαn with 0 ≤ αn → ∞ and ∑ |cn|rαn < ∞ for some r > 1 is definable. This expansion is polynomially bounded.

KW - Blowing-up

KW - Model completeness

KW - O-minimal structures

KW - Power series

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The real field with convergent generalized power series

Abstract

Keywords

ASJC Scopus subject areas

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