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Set Theory (Studies in Logic: Mathematical Logic and Foundations) de Kenneth Kunen
Descripción - Reseña del editor This book is designed for readers who know elementary mathematical logic and axiomatic set theory, and who want to learn more about set theory. The primary focus of the book is on the independence proofs. Most famous among these is the independence of the Continuum Hypothesis (CH); that is, there are models of the axioms of set theory (ZFC) in which CH is true, and other models in which CH is false. More generally, cardinal exponentiation on the regular cardinals can consistently be anything not contradicting the classical theorems of Cantor and König. The basic methods for the independence proofs are the notion of constructibility, introduced by Gödel, and the method of forcing, introduced by Cohen. This book describes these methods in detail, verifi es the basic independence results for cardinal exponentiation, and also applies these methods to prove the independence of various mathematical questions in measure theory and general topology. Before the chapters on forcing, there is a fairly long chapter on 'infi nitary combinatorics'. This consists of just mathematical theorems (not independence results), but it stresses the areas of mathematics where set-theoretic topics (such as cardinal arithmetic) are relevant. There is, in fact, an interplay between infi nitary combinatorics and independence proofs. Infi nitary combinatorics suggests many set-theoretic questions that turn out to be independent of ZFC, but it also provides the basic tools used in forcing arguments. In particular, Martin's Axiom, which is one of the topics under infi nitary combinatorics, introduces many of the basic ingredients of forcing.
Detalles del Libro
- Name: Set Theory (Studies in Logic: Mathematical Logic and Foundations)
- Autor: Kenneth Kunen
- Categoria: Libros,Ciencias, tecnología y medicina,Matemáticas
- Tamaño del archivo: 18 MB
- Tipos de archivo: PDF Document
- Idioma: Español
- Archivos de estado: AVAILABLE
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Set Theory Studies in Logic: Mathematical Logic and ~ INITIAL REVIEW This will be a short initial review prior to reading any of this very recently acquired book. This book by master expositor Kenneth Kunen, emeritus at University of Wisconsin-Madison, is a newly rewritten 2011 update of his well regarded, rather standard 1980 edition, still available at Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of .
Elements of Set Theory by Herbert B. Enderton - Books on ~ Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics.
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Set Theory (Studies in Logic: Mathematical Logic and ~ Long chapter I called 'Background Material' is rather similar to great chapter I on ZFC set theory in Kunen's excellent 2009 book The Foundations of Mathematics (Logic S.), which I have read thru 100 page chapter II on model theory and proof theory, with chapter II twice, and finally read short chapter III on philosophy of math.
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Paul Bernays - Wikipedia, la enciclopedia libre ~ Bernays, Paul (1958), Axiomatic set theory, Studies in Logic and the Foundations of Mathematics (en inglés), Amsterdam: North-Holland, ISBN 978-0-486-66637-2, MR 0106178 Bernays, Paul (1976), Abhandlungen zur Philosophie der Mathematik (en alemán), Darmstadt: Wissenschaftliche Buchgesellschaft, ISBN 978-3-534-06706-0, MR 0444417
Teoría de conxuntos - Wikipedia, a enciclopedia libre ~ Os tópicos matemáticos xorden e desenvólvense frecuentemente pola interacción de moitos investigadores. Porén, a teoría de conxuntos fundouna un único matemático, Georg Cantor, cando, en 1874 publicou o artigo "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen" ("Sobre unha propiedade característica de todos os números reais alxébricos") [1] [2].
Teoría da computabilidade - Wikipedia, a enciclopedia libre ~ Recursively Enumerable Sets and Degrees, Perspectives in Mathematical Logic, Springer-Verlag. ISBN 0-387-15299-7. K. Ambos os-Spies and P. Fejer, 2006. "Degrees of Unsolvability." Unpublished preprint. H. Enderton, 1977. "Elements of Recursion Theory." Handbook of Mathematical Logic, edited by J. Barwise, North-Holland (1977), pp. 527–566.
Zermelo's Axiom of Choice: Its Origins, Development, and ~ Over the last couple of years, I have collected some 45 books on set theory and mathematical logic, trying to understand the significance of the axiom of choice. With this book, Zermelo's Axiom of Choice: Its Origins, Development, and Influence , by Gregory H. Moore, many of my questions about the axiom of choice were answered within a few minutes of turning the pages.
Willard Van Orman Quine - Wikipedia, a enciclopedia libre ~ Lóxica elemental (Elementary Logic). 1941. O sentido da nova lóxica (O Sentido da Nova Lógica). 1944. Os métodos da lóxica (Methods of Logic). 1950. Desde un punto de vista lóxico (From a Logical Point of View). 1953. Palabra e obxecto (Word and Object). 1960. La teoría de conxuntos e a súa lóxica (Set Theory and Its Logic). 1963.
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George Boolos - Wikipedia, la enciclopedia libre ~ Frege's Philosophy of Mathematics. Harvard Univ. Press. 1968 (with Hilary Putnam), "Degrees of unsolvability of constructible sets of integers," Journal of Symbolic Logic 33: 497-513. 1969, "Effectiveness and natural languages" in Sidney Hook, ed., Language and Philosophy. New York University Press.
Adolf Fraenkel - Wikipedia, la enciclopedia libre ~ Abraham Halevi «Adolf» Fraenkel (en hebreo, אברהם הלוי "אדולף" פרנקל ; Múnich, 17 de febrero de 1891 - Jerusalén, 15 de octubre de 1965) fue un lógico y matemático alemán nacionalizado israelí.. Estudió matemáticas en las universidades de Múnich, Berlín, Marburgo y Breslau.Después de su graduación dio clases en la Universidad de Marburgo desde 1916 donde .