Elimination of quantifiers of linear variables and corresponding transfer principles
B. Curtis Eaves, Uriel G. Rothblum · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1987
Given a first order formula for ordered fields whose quantified variables are linear with respect to each other, we show how to eliminate the quantifiers and obtain a quantifier-free formula that is equivalent to the original one over all ordered fields. The result parallels Tarski's Theorem that concerns the elimination of quantifiers for first order formula for ordered fields applied to real closed fields. Like Tarski's Theorem, our results yield transfer principles for drawing conclusions in one ordered field that are established for another. Applications of this transfer principle are discussed. 9 refs.