Erratum to "Fields of surreal numbers and exponentiation" (Fund. Math. 167 (2001), 173-188)
Lou van den Dries, Philip Ehrlich (2001)
Fundamenta Mathematicae
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Lou van den Dries, Philip Ehrlich (2001)
Fundamenta Mathematicae
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Paola D'Aquino, Angus Macintyre, Giuseppina Terzo (2010)
Fundamenta Mathematicae
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We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.
Helmut Wolter (1984)
Mémoires de la Société Mathématique de France
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Lou van den Dries, Philip Ehrlich (2001)
Fundamenta Mathematicae
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We show that Conway's field of surreal numbers with its natural exponential function has the same elementary properties as the exponential field of real numbers. We obtain ordinal bounds on the length of products, reciprocals, exponentials and logarithms of surreal numbers in terms of the lengths of their inputs. It follows that the set of surreal numbers of length less than a given ordinal is a subfield of the field of all surreal numbers if and only if this ordinal is an ε-number....
M. Stojaković (1972)
Publications de l'Institut Mathématique
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Irving Stringham (1893)
Bulletin of the New York Mathematical Society
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E. Bombieri (1978)
Inventiones mathematicae
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Garyfalos Papaschinopoulos, John Schinas (1985)
Czechoslovak Mathematical Journal
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Chaves, Max, Singleton, Douglas (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Yong-Gao Chen, Jin-Hui Fang, Norbert Hegyvári (2016)
Acta Arithmetica
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Ding, Ping (2005)
Journal of Mathematical Sciences (New York)
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Paola D'Aquino, Julia F. Knight, Salma Kuhlmann, Karen Lange (2012)
Fundamenta Mathematicae
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Ressayre considered real closed exponential fields and “exponential” integer parts, i.e., integer parts that respect the exponential function. In 1993, he outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre’s construction and then analyze the complexity. Ressayre’s construction is canonical once we fix the real closed exponential field R, a residue field section k, and a well ordering...
Marinkovic, Sladjana, Stankovic, Miomir, Mulalic, Edin (2012)
Mathematica Balkanica New Series
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MSC 2010: 33B10, 33E20 Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner,...
Bachman, Gennady (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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