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A PSEUDOEXPONENTIAL-LIKE STRUCTURE ON THE ALGEBRAIC NUMBERS

Published online by Cambridge University Press:  22 December 2015

VINCENZO MANTOVA
VINCENZO MANTOVA*
Affiliation:
DIVISION OF MATHEMATICS, SCHOOL OF SCIENCE AND TECHNOLOGY UNIVERSITY OF CAMERINO VIA MADONNA DELLE CARCERI 9, 62032, CAMERINO (MC)ITALYE-mail: vincenzo.mantova@unicam.it
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Abstract

Pseudoexponential fields are exponential fields similar to complex exponentiation which satisfy the Schanuel Property, i.e., the abstract statement of Schanuel’s Conjecture, and an adapted form of existential closure.

Here we show that if we remove the Schanuel Property and just care about existential closure, it is possible to create several existentially closed exponential functions on the algebraic numbers that still have similarities with complex exponentiation. The main difficulties are related to the arithmetic of algebraic numbers, and they can be overcome with known results about specialisations of multiplicatively independent functions on algebraic varieties.

Keywords

exponential fieldsexponential-algebraic closuremultiplicative dependencies
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 4 , December 2015 , pp. 1339 - 1347
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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