The first English translation of the well-received French text "Corps et Modeles," "Fields and Models: from Sturm to Tarski and Robinson" traces the intertwined development of logic and algebra, particularly Tarski's model theory and Artin's and Schrier's algebra of real-closed fields. A number of pivotal results are woven in to this collaboration across disciplines: Sturm's theorem on the location of roots of real polynomials, which is the unifying theme, as well as Artin's solution to Hilbert's 17th problem, Tarski's decision procedure for the field of real numbers, and research into quadratic forms. Drawing extensively on original sources, Hourya Sinaceur discusses not only the evolution of new mathematical ideas, but also their epistemological foundations and the ways in which mathematical subdisciplines influence one another. A wide audience of students and researchers in both the sciences and humanities will benefit from this fascinating chapter of intellectual history.
Foreword.- Mathematical Symbols and Abbreviations.- Introduction.- I. C.F. Sturm's Theorem of Algebra.- II. The Algebraic Construction of Real Fields by Emil Artin and Otto Schreier.- III. Real Algebra and the Theory of Quadratic Forms.- IV. Logic and Real Algebra.- General Conclusion.- Glossary.- Bibliography Relevant to Sturm's Theorem of Algebra.- General Bibliography.- Index.