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Author: John R. Steel
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 119
ISBN-13: 1107167965
DOWNLOAD EBOOK →Suitable for graduate students and researchers in set theory, this volume develops a method for constructing core models that have Woodin cardinals.
Author: John R. Steel
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 120
ISBN-13: 1316739287
DOWNLOAD EBOOK →Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Large cardinal hypotheses play a central role in modern set theory. One important way to understand such hypotheses is to construct concrete, minimal universes, or 'core models', satisfying them. Since Gödel's pioneering work on the universe of constructible sets, several larger core models satisfying stronger hypotheses have been constructed, and these have proved quite useful. In this volume, the eighth publication in the Lecture Notes in Logic series, Steel extends this theory so that it can produce core models having Woodin cardinals, a large cardinal hypothesis that is the focus of much current research. The book is intended for advanced graduate students and researchers in set theory.
Author: Matthew Foreman
Publisher: Springer Science & Business Media
Published: 2009-12-10
Total Pages: 2200
ISBN-13: 1402057644
DOWNLOAD EBOOK →Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Author: William J. Mitchell
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 138
ISBN-13: 1316763854
DOWNLOAD EBOOK →Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the third publication in the Lecture Notes in Logic series, Mitchell and Steel construct an inner model with a Woodin cardinal and develop its fine structure theory. This work builds upon the existing theory of a model of the form L[E], where E is a coherent sequence of extenders, and relies upon the fine structure theory of L[E] models with strong cardinals, and the theory of iteration trees and 'backgrounded' L[E] models with Woodin cardinals. This work is what results when fine structure meets iteration trees.
Author: Haim Judah
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 417
ISBN-13: 1461397545
DOWNLOAD EBOOK →Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.
Author: S. Barry Cooper
Publisher: Cambridge University Press
Published: 1999-06-17
Total Pages: 450
ISBN-13: 9780521635493
DOWNLOAD EBOOK →First of two volumes providing a comprehensive guide to mathematical logic.
Author:
Publisher: Elsevier
Published: 2012-01-24
Total Pages: 878
ISBN-13: 0080930662
DOWNLOAD EBOOK →Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights
Author: John R. Steel
Publisher: Cambridge University Press
Published: 2022-11-24
Total Pages: 550
ISBN-13: 1108896820
DOWNLOAD EBOOK →This book proves some important new theorems in the theory of canonical inner models for large cardinal hypotheses, a topic of central importance in modern set theory. In particular, the author 'completes' the theory of Fine Structure and Iteration Trees (FSIT) by proving a comparison theorem for mouse pairs parallel to the FSIT comparison theorem for pure extender mice, and then using the underlying comparison process to develop a fine structure theory for strategy mice. Great effort has been taken to make the book accessible to non-experts so that it may also serve as an introduction to the higher reaches of inner model theory. It contains a good deal of background material, some of it unpublished folklore, and includes many references to the literature to guide further reading. An introductory essay serves to place the new results in their broader context. This is a landmark work in inner model theory that should be in every set theorist's library.
Author: Zoe Chatzidakis
Publisher: CRC Press
Published: 2006-07-13
Total Pages: 370
ISBN-13: 1439865906
DOWNLOAD EBOOK →Logic Colloquium '02 includes articles from some of the world's preeminent logicians. The topics span all areas of mathematical logic, but with an emphasis on Computability Theory and Proof Theory. This book will be of interest to graduate students and researchers in the field of mathematical logic.
Author: C T Chong
Publisher: World Scientific
Published: 1998-04-04
Total Pages: 368
ISBN-13: 9814496294
DOWNLOAD EBOOK →This volume collects written versions of invited and contributed talks presented at the conference. It covers many areas of logic and the foundations of mathematics, as well as computer science. Contents:Seminormal Fine Measures on Pκ(λ) (Y Abe)Effective Baire Category Concepts (K Ambos-Spies & J Reimann)Weak Presentations of Computable Partial Orderings (M M Arslanov & I S Kalimullin)Recursion Theory and Weak Fragments of Peano Arithmetic: A Study of Definable Cuts (C T Chong & Y Yang)Lattice Embedding into d-r.e. Degrees Preserving 0 and 1 (D Ding & L Qian)On Stationary Reflection Principles (Q Feng)Definable Sets of Real Numbers, Infinite Games and Core Model Theory (K Hauser)The Descriptive Classification of Some Classes of C∗-Algebras (A S Kechris)Decidability and Undecidability in the Enumerable Turing Degrees (S Lempp)The Theory of Finite Models (L Luo)A Note on Weak Segments of PFA (T Miyamoto)On Structural Inference Rules for Gentzen-Style Natural Deduction, Part I (K Nakatogawa)Linear Set Theory with Strict Comprehension (M Shirahata)A Solution to a Problem of Marek and Truszcynski (K Su & H Chen)Credulous Reasoning About Defaults (Y H Tan & L W N van der Torre)Computational Complexity of Infinite-Valued Lukasiewicz Propositional Logic (H Wagner)DNK and Natural Reasoning (M Yasugi & M Nakata)Default Logic and Its Variants: A Semantical View (M Zhang)Adding Eventual Different Reals (Y Zhang)Asian Logic Conferences (M Yasugi) Readership: Logicians, computer scientists, graduate students and research mathematicians. Keywords:Seminormal Fine Measures;Baire Category;Computable Partial Orderings;Recursion Theory;Peano Arithmetic;Core Model Theory;Câ-Algebras;Finite Models;Natural Reasoning;Default Logic
