The Collected Works of Julia Robinson
This volume presents all the published works -- spanning more than thirty years -- of Julia Bowman Robinson. These papers constitute important contributions to the theory of effectively calculable functions and to its applications. Outstanding among the latter are Robinson's proof of the effective unsolvability of the decision problem for the rational number field (and, consequently of that for the first-order theory of all fields), and her work that provided the central step toward the negative solution of Hilbert's Tenth Problem. These results provide upper bound for what one can hope to obtain in the way of positive solutions to the decision problem for special classes of fields and for special classes of diophantine equations, respectively. Besides thematic unity, Robinson's papers are distinguished by their clarity of purpose and accessibility to non-specialists as well as specialists. The volume also includes an extensive biographical memoir on the life and work of Robinson, who will be remembered not only for her distinctive and vital contributions, but also as the first woman to be elected to the mathematical section of the National Academy of Sciences and as the first woman to be President of the American Mathematical Society.
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Common terms and phrases
a₁ algebraic integers algorithm Amer arbitrary diophantine equation arithmetical formula arithmetically definable assumes all values COROLLARY decision problem definable in terms Diophantine definition diophantine relation Diophantine set equa equivalent existentially definable exponential diophantine equation finite number finite set function F functional equations G₁ given Gödel Hence Hilbert's tenth problem holds hyperarithmetical hypothesis induction initial functions integer coefficients Julia Robinson Kleene Lemma listable set Math mathematical Matijasevič natural numbers number theory obtained p-adic P₁ pairing functions parameters polynomial positive integers primitive recursive functions proof proved Putnam quantifiers R. M. Robinson range rational numbers real closed field recursively enumerable relation recursively enumerable set relatively prime result satisfies Section set of natural set of primes solution solvable Suppose symbols system of equations Tarski tion U₁ undecidable unique function unknowns unsolvable x₁ zero
References to this book
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Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry ... Jan Denef No preview available - 2000 |