Computable valued fields |
| |
Authors: | Matthew Harrison-Trainor |
| |
Institution: | 1.Group in Logic and the Methodology of Science,University of California,Berkeley,USA;2.Department of Pure Mathematics,University of Waterloo,Waterloo,Canada |
| |
Abstract: | We investigate the computability-theoretic properties of valued fields, and in particular algebraically closed valued fields and p-adically closed valued fields. We give an effectiveness condition, related to Hensel’s lemma, on a valued field which is necessary and sufficient to extend the valuation to any algebraic extension. We show that there is a computable formally p-adic field which does not embed into any computable p-adic closure, but we give an effectiveness condition on the divisibility relation in the value group which is sufficient to find such an embedding. By checking that algebraically closed valued fields and p-adically closed valued fields of infinite transcendence degree have the Mal’cev property, we show that they have computable dimension \(\omega \). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|