A pseudoexponentiation-like structure on the algebraic numbers
Number Theory
2017-02-01 v2 Logic
Abstract
Pseudoexponential fields are exponential fields similar to complex exponentiation satisfying the Schanuel Property, which is 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.
Cite
@article{arxiv.1202.4022,
title = {A pseudoexponentiation-like structure on the algebraic numbers},
author = {Vincenzo Mantova},
journal= {arXiv preprint arXiv:1202.4022},
year = {2017}
}
Comments
8 pages. Several stylistic edits and updated bibliography