Displaying similar documents to “Fields of surreal numbers and exponentiation”

Real closed exponential fields

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...

Schanuel Nullstellensatz for Zilber fields

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.