A pseudoexponentiation-like structure on the algebraic numbers

Submitted by Vincenzo Mantova on Wed, 22/02/2012 - 20:10
TitleA pseudoexponentiation-like structure on the algebraic numbers
Publication TypeJournal Article
Year of Publication2015
AuthorsMantova, V
JournalJournal of Symbolic Logic
Date Published2015/12

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 can be overcome with known results about specialisations of multiplicatively independent functions on algebraic varieties.

Refereed DesignationRefereed