  View Basket     AiML Algorithmics Cadernos de Lógica e Computação Cadernos de Lógica e Filosofia Cahiers de Logique et d'Epistemologie Communication, Mind and Language Computing Cuadernos de lógica, Epistemología y Lenguaje DEON Dialogues Economics Encyclopaedia of Logic Filosofia Handbooks Historia Logicae IfColog series in Computational Logic Journals Journal of Applied Logics - IfCoLoG Journal of Logics and their Applications Law Logic and Semiotics Logic PhDs Logic, Methodology and Philosophy of Science The Logica Yearbook Neural Computing and Artificial Intelligence Philosophy Research The SILFS series Studies in Logic History of Logic Logic and cognitive systems Mathematical logic and foundations Studies in Logic and Argumentation Studies in Talmudic Logic Systems Texts in Logic and Reasoning Texts in Mathematics Tributes Other Digital Downloads Information for authors About us Search for Books  Mathematical logic and foundations Back The Foundations of MathematicsKenneth KunenMathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Löwenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H(κ) and R(γ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Gödel, and Tarski's theorem on the non-definability of truth. 8 September 2009978-1-904987-14-7Buy from Amazon: UK   US

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