Woodin, W. H. (W. Hugh)
Overview
Works:  17 works in 120 publications in 2 languages and 6,635 library holdings 

Genres:  Conference papers and proceedings History Academic theses 
Roles:  Editor, Author, Honoree, Thesis advisor 
Publication Timeline
.
Most widely held works by
W. H Woodin
An introduction to independence for analysts by
H. G Dales(
Book
)
23 editions published between 1987 and 2008 in English and held by 375 WorldCat member libraries worldwide
Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC
23 editions published between 1987 and 2008 in English and held by 375 WorldCat member libraries worldwide
Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC
The axiom of determinacy, forcing axioms, and the nonstationary ideal by
W. H Woodin(
Book
)
31 editions published between 1999 and 2011 in English and German and held by 245 WorldCat member libraries worldwide
The starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the nonstationary ideal on [omega]1; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universalexistential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method. This monograph is directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of [Omega]logic and related matters
31 editions published between 1999 and 2011 in English and German and held by 245 WorldCat member libraries worldwide
The starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the nonstationary ideal on [omega]1; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universalexistential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method. This monograph is directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of [Omega]logic and related matters
Superreal fields : totally ordered fields with additional structure by
H. G Dales(
Book
)
8 editions published in 1996 in English and held by 244 WorldCat member libraries worldwide
8 editions published in 1996 in English and held by 244 WorldCat member libraries worldwide
Infinity : new research frontiers by
Michał Heller(
Book
)
14 editions published between 2011 and 2013 in English and Undetermined and held by 241 WorldCat member libraries worldwide
"'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (18621943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen worldrenowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity"Provided by publisher
14 editions published between 2011 and 2013 in English and Undetermined and held by 241 WorldCat member libraries worldwide
"'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (18621943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen worldrenowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity"Provided by publisher
Set theory of the continuum by
H Judah(
Book
)
12 editions published in 1992 in English and held by 179 WorldCat member libraries worldwide
Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 198990, 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 settheoretic 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
12 editions published in 1992 in English and held by 179 WorldCat member libraries worldwide
Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 198990, 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 settheoretic 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
Foundations of mathematics : logic at Harvard : essays in honor of Hugh Woodin's 60th birthday, March 2729, 2015, Harvard
University, Cambridge, MA by Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday(
Book
)
5 editions published in 2017 in English and held by 65 WorldCat member libraries worldwide
5 editions published in 2017 in English and held by 65 WorldCat member libraries worldwide
Notes on forcing axioms by
Stevo Todorcevic(
Book
)
3 editions published in 2014 in English and held by 48 WorldCat member libraries worldwide
In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the BanachSteinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the settheoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions
3 editions published in 2014 in English and held by 48 WorldCat member libraries worldwide
In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the BanachSteinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the settheoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions
Infinity and truth by
Qi Feng(
Book
)
6 editions published between 2013 and 2014 in English and Undetermined and held by 45 WorldCat member libraries worldwide
This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters are by leading experts in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable within the ZermeloFraenkel set theory with the axiom of choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progresses in foundational studies. The final chapter features questions proposed by the participants of the workshop that will drive foundational research. The wide range of topics covered here will be of benefit to students, researchers and mathematicians interested in the foundations of mathematics
6 editions published between 2013 and 2014 in English and Undetermined and held by 45 WorldCat member libraries worldwide
This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters are by leading experts in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable within the ZermeloFraenkel set theory with the axiom of choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progresses in foundational studies. The final chapter features questions proposed by the participants of the workshop that will drive foundational research. The wide range of topics covered here will be of benefit to students, researchers and mathematicians interested in the foundations of mathematics
Forcing, iterated ultrapowers, and Turing degrees by Asian Initiative for Infinity (AII) Graduate Logic Summer School(
Book
)
6 editions published between 2015 and 2016 in English and held by 33 WorldCat member libraries worldwide
The lecture notes in mathematical logic from the 2010 and 2011 Asian Initiative for Infinity Logic Summer Schools
6 editions published between 2015 and 2016 in English and held by 33 WorldCat member libraries worldwide
The lecture notes in mathematical logic from the 2010 and 2011 Asian Initiative for Infinity Logic Summer Schools
Discontinuous homomorphisms of C(omega) and set theory by
W. H Woodin(
)
4 editions published in 1984 in English and held by 9 WorldCat member libraries worldwide
The main question considered is a problem of Kaplansky. Suppose (OMEGA) is a compact Hausdorff space and let C((OMEGA)) denote the Banach algebra of continous complex valued functions with domain (OMEGA). The norm is the usual supnorm; for f in C((OMEGA)), (VBAR)(VBAR)f(VBAR)(VBAR) = sup (VBAR)f(x)(VBAR) (VBAR) x (ELEM) (OMEGA) . Assume (LAMDA) : C((OMEGA)) ( >) B is a homomorphism of C((OMEGA)) into an arbitrary Banach algebra, B. Is (LAMDA) continuous?
4 editions published in 1984 in English and held by 9 WorldCat member libraries worldwide
The main question considered is a problem of Kaplansky. Suppose (OMEGA) is a compact Hausdorff space and let C((OMEGA)) denote the Banach algebra of continous complex valued functions with domain (OMEGA). The norm is the usual supnorm; for f in C((OMEGA)), (VBAR)(VBAR)f(VBAR)(VBAR) = sup (VBAR)f(x)(VBAR) (VBAR) x (ELEM) (OMEGA) . Assume (LAMDA) : C((OMEGA)) ( >) B is a homomorphism of C((OMEGA)) into an arbitrary Banach algebra, B. Is (LAMDA) continuous?
Slicing the truth : on the computable and reverse mathematics of combinatorial principles by
Denis Roman Hirschfeldt(
Book
)
2 editions published in 2015 in English and held by 2 WorldCat member libraries worldwide
This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a casestudy approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions
2 editions published in 2015 in English and held by 2 WorldCat member libraries worldwide
This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a casestudy approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions
Homogeneous sequences of cardinals for ordinal definable partition relations by George Kafkoulis(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
The stationary tower : notes on a course by W. Hugh Woodin by
Paul B Larson(
Book
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
"This book is suitable for a graduate course that assumes some familiarity with forcing, constructibility, and ultrapowers. It is also recommended for researchers interested in logic, set theory, and forcing."BOOK JACKET
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
"This book is suitable for a graduate course that assumes some familiarity with forcing, constructibility, and ultrapowers. It is also recommended for researchers interested in logic, set theory, and forcing."BOOK JACKET
Independence results for indescribable cardinals by Kai Hauser(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Descriptive set theory and forcing : how to prove theorems about Borel sets the hard way by
Arnold W Miller(
)
1 edition published in 1995 in English and held by 0 WorldCat member libraries worldwide
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 fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis
1 edition published in 1995 in English and held by 0 WorldCat member libraries worldwide
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 fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis
One hundred years of Russell's paradox : mathematics, logic, philosophy(
)
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
"The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the abovementioned fields. The volume contributes thereby to the wellestablished body of mathematical philosophy initiated to a large extent by Russell's work."Jacket
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
"The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the abovementioned fields. The volume contributes thereby to the wellestablished body of mathematical philosophy initiated to a large extent by Russell's work."Jacket
Logic Colloquium '96 : proceedings of the colloquium held in San Sebastián, Spain, July 915, 1996 by
Jesús M Larrazabal(
)
1 edition published in 1998 in English and held by 0 WorldCat member libraries worldwide
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. This volume, the twelfth publication in the 'Lecture Notes in Logic' series, collects the proceedings of the European Summer Meeting of the Association of Symbolic Logic, held at the University of the Basque Country, San Sebastian in July 1996. The main topics were model theory, proof theory, recursion and complexity theory, models of arithmetic, logic for artificial intelligence, formal semantics of natural language, and philosophy of contemporary logic. The volume includes eleven papers from preeminent researchers in mathematical logic
1 edition published in 1998 in English and held by 0 WorldCat member libraries worldwide
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. This volume, the twelfth publication in the 'Lecture Notes in Logic' series, collects the proceedings of the European Summer Meeting of the Association of Symbolic Logic, held at the University of the Basque Country, San Sebastian in July 1996. The main topics were model theory, proof theory, recursion and complexity theory, models of arithmetic, logic for artificial intelligence, formal semantics of natural language, and philosophy of contemporary logic. The volume includes eleven papers from preeminent researchers in mathematical logic
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Related Identities
 Feng, Qi 1955 Author Editor
 Slaman, T. A. (Theodore Allen) 1954 Editor
 Chong, C.T (ChiTat) 1949 Editor
 Dales, H. G. (Harold G.) 1944 Author
 Yang, Yue 1964 Editor
 Todorcevic, Stevo Author
 Heller, Michał Author Editor
 Just, W. (Winfried) Editor
 Judah, H. (Haim) Author Editor
 Mathematical Sciences Research Institute (Berkeley, Calif.) Editor
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Associated Subjects
Axiomatic set theory Axioms Baire classes Borel sets Cardinal numbers Combinatorial analysis Computer science Continuum hypothesis Forcing (Model theory) Independence (Mathematics) Infinite Liar paradox Logic Logic, Symbolic and mathematical Mathematics MathematicsPhilosophy Model theory Ordered fields Paradox Reverse mathematics Set theory Unsolvability (Mathematical logic)
Alternative Names
W. Hugh Woodin Amerikaans wiskundige
W. Hugh Woodin amerikansk matematikar
W. Hugh Woodin amerikansk matematiker
W. Hugh Woodin matemático estadounidense
W. Hugh Woodin matematico statunitense
W. Hugh Woodin mathématicien américain
W. Hugh Woodin USamerikanischer Mathematiker
William Hugh Woodin
Woodin, H.
Woodin, H. 1945
Woodin, H. (Hugh)
Woodin, Hugh
Woodin, Hugh 1945
Woodin, W. H.
Woodin, W. H. 1945
Woodin, William H. 1945
Woodin, William Hugh 1945
Wooding Hug
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