Mantova, V orcid.org/0000-0002-8454-7315 (2015) A pseudoexponential-like structure on the algebraic numbers. The Journal of Symbolic Logic, 80 (04). pp. 1339-1347. ISSN 0022-4812
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Association for Symbolic Logic 2015. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Jul 2017 15:40 |
Last Modified: | 26 Jul 2017 15:40 |
Status: | Published |
Publisher: | Association for Symbolic Logic |
Identification Number: | 10.1017/jsl.2014.41 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:115289 |