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Decidable fragments of field theories

Published online by Cambridge University Press:  12 March 2014

Shih-Ping Tung
Shih-Ping Tung*
Affiliation:
Department of Mathematics, Chung-Yuan Christian University, Chung Li, Taiwan 320-23, Republic of China
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Abstract

We say φ is an ∀∃ sentence if and only if φ is logically equivalent to a sentence of the form ∀x∃yψ(x, y), where ψ(x, y) is a quantifier-free formula containing no variables except x and y. In this paper we show that there are algorithms to decide whether or not a given ∀∃ sentence is true in (1) an algebraic number field K, (2) a purely transcendental extension of an algebraic number field K, (3) every field with characteristic 0, (4) every algebraic number field, (5) every cyclic (abelian, radical) extension field over Q, and (6) every field.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 3 , September 1990 , pp. 1007 - 1018
Copyright
Copyright © Association for Symbolic Logic 1990

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