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This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed.Originally published in 1986.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Constructive mathematics. --- Arithmetic. --- Mathematics --- Set theory --- Calculators --- Numbers, Real --- Mathematics, Constructive --- Logic, Symbolic and mathematical --- Addition. --- Adjunction (field theory). --- Age of the universe. --- Almost surely. --- Arithmetic IF. --- Atomic formula. --- Axiom. --- Axiomatic system. --- Beta function. --- Big O notation. --- Binary number. --- Binary relation. --- Brownian motion. --- Canonical form. --- Cardinality. --- Cartesian coordinate system. --- Chessboard. --- Classical mathematics. --- Closed-form expression. --- Commutative property. --- Computation. --- Conservative extension. --- Consistency. --- Contradiction. --- Deduction theorem. --- Diameter. --- Direct proof. --- Domain of discourse. --- Elementary mathematics. --- Elias M. Stein. --- Existential quantification. --- Exponential function. --- Exponentiation. --- Extension by definitions. --- Finitary. --- Finite set. --- Formula C (SCCA). --- Foundations of mathematics. --- Fundamenta Mathematicae. --- Gödel's completeness theorem. --- Herbrand's theorem. --- Impredicativity. --- Inaccessible cardinal. --- Inference. --- Interpretability. --- John Milnor. --- Logic. --- Logical connective. --- Mathematical induction. --- Mathematical logic. --- Mathematician. --- Mathematics. --- Measurable cardinal. --- Metamathematics. --- Metatheorem. --- Model theory. --- Mostowski. --- Natural number. --- Negation. --- Non-standard analysis. --- Notation. --- P-adic analysis. --- Peano axioms. --- Polynomial. --- Positional notation. --- Power of two. --- Power set. --- Primitive notion. --- Primitive recursive function. --- Principia Mathematica. --- Probability theory. --- Quantifier (logic). --- Quantity. --- Ranking (information retrieval). --- Rational number. --- Real number. --- Recursion (computer science). --- Remainder. --- Requirement. --- Robert Langlands. --- Rule of inference. --- Scientific notation. --- Sequence. --- Set theory. --- Subset. --- Theorem. --- Theory. --- Transfer principle. --- Transfinite number. --- Triviality (mathematics). --- Tuple. --- Uniqueness. --- Universal quantification. --- Variable (mathematics). --- Zermelo–Fraenkel set theory.