A Decision Method for Elementary Algebra and GeometryThis revised edition of A Decision Method for Elementary Algebra and Geometry presents the culmination of research begun in 1930, which laid foundational results in algebraic and geometric completeness. Originally intended for publication in 1939 by Hermann & Cie, Paris, the onset of war delayed its release, with only proofs left as a record. The RAND Corporation's interest in 1948 revived the project, resulting in a monograph focused on the systematic development of a decision method for elementary algebra and geometry, emphasizing its practical potential in creating a decision-making machine. Under the editorial guidance of Professor J.C.C. McKinsey, this work was refined with a new draft, clarifying key theoretical aspects and introducing simplifications to the development process. The current edition reproduces RAND's publication with minor corrections, updated references, and supplementary notes that expand upon original theories, including fresh bibliographical insights. This title was originally published in 1951. Many titles in the Voices Revived program are also newly available as ebooks, offered at a discounted price to support wider access to scholarly work. |
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algebra and geometry algebraic closed fields algebraic constants algebraic terms applies arithmetically definable atomic formula axiom axiomatic axions construction correlated De(a decision machine decision method decision problem Definition 22 denote discussion disjunction elementary algebra elementary geometry elementary theory equations and inequalities equivalent formula establish Euclidean geometry example fact finite number form 28 formula of order forn free variables function given hence induction instance integer introduce intuitive involve Journal of symbolic leading coefficient McKinsey means metamathematical method for elementary monograph non-negative integer notion of truth number of roots obtained open interval operator particular Phoor polynomial of degree positive and odd proof provable sentence real closed field real numbers recursive relation represent arbitrary right-hand end-point satisfied Section sentence of elementary sentential calculus sequence simply solution system of elementary Tarski tern theorem Theoren 27 Theoren 31 true sentences values vanish identically zero ΑΕ εξ