Pseudo-exponentiation on algebraically closed fields of characteristic zero
The author introduces the strongly exponentially-algebraically closed fields with pseudo-ex\-po\-nen\-tia\-tion as structures very close to \(C_{\exp}\), the field of complex numbers with exponentiation, and gives a natural (non first-order) axiomatization for them. One of the main results of the paper is a categoricity theorem stating that there is, up to isomorphism, exactly one such structure of a given uncountable cardinality. It is shown that the well-known Schanuel conjecture and a conjecture stating that certain systems of exponential equations over complex numbers do have solutions in the complex numbers are the conditions under which \(C_{\exp}\) is the corresponding structure of continuum cardinality.
scientific article; zbMATH DE number 2126478