Some remarks on Schanuel's conjecture

✍ Scribed by Ricardo Bianconi

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 71 KB
• Volume: 108
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(00)00039-7

✦ Synopsis

Schanuel's Conjecture is the statement: if x1; : : : ; xn ∈ C are linearly independent over Q, then the transcendence degree of Q(x1; : : : ; xn; exp(x1); : : : ; exp(xn)) over Q is at least n. Here we prove that this is true if instead we take inÿnitesimal elements from any ultrapower of C, and in fact from any nonarchimedean model of the theory of the expansion of the ÿeld of real numbers by restricted analytic functions.