Woodin, W. H. (W. Hugh)
Overview
Works:  21 works in 116 publications in 2 languages and 6,198 library holdings 

Genres:  History Conference papers and proceedings Academic theses 
Roles:  Editor, Author, Thesis advisor 
Classifications:  QA9.7, 511.322 
Publication Timeline
.
Most widely held works by
W. H Woodin
An introduction to independence for analysts by
H. G Dales(
Book
)
22 editions published between 1987 and 2008 in English and Undetermined and held by 376 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
22 editions published between 1987 and 2008 in English and Undetermined and held by 376 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 244 WorldCat member libraries worldwide
This is the revised and updated second edition of a wellestablished research monograph on the axiom of determinacy, written by an expert in the field. This axiom is a fundamental statement in set theory, and it is related to winning strategies in game theory
31 editions published between 1999 and 2011 in English and German and held by 244 WorldCat member libraries worldwide
This is the revised and updated second edition of a wellestablished research monograph on the axiom of determinacy, written by an expert in the field. This axiom is a fundamental statement in set theory, and it is related to winning strategies in game theory
Superreal fields : totally ordered fields with additional structure by
H. G Dales(
Book
)
8 editions published in 1996 in English and held by 243 WorldCat member libraries worldwide
8 editions published in 1996 in English and held by 243 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 226 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 226 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
Notes on forcing axioms by
Stevo Todorcevic(
Book
)
3 editions published in 2014 in English and held by 46 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 rather than on the relationship between different forcing axioms or their consistency strengths
3 editions published in 2014 in English and held by 46 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 rather than on the relationship between different forcing axioms or their consistency strengths
Infinity and truth by
Qi Feng(
Book
)
5 editions published in 2014 in English and Undetermined and held by 43 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
5 editions published in 2014 in English and Undetermined and held by 43 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
)
5 editions published between 2015 and 2016 in English and held by 28 WorldCat member libraries worldwide
The lecture notes in mathematical logic from the 2010 and 2011 Asian Initiative for Infinity Logic Summer Schools
5 editions published between 2015 and 2016 in English and held by 28 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?
The Borel Conjecture by
Calif.) Mathematical Sciences Research Institute (Berkeley(
Book
)
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
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
Notes On Forcing Axioms by
W. H Woodin(
Book
)
1 edition published in 2014 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 2014 in Undetermined 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
The stationary tower is an important method in modern set theory, invented by Hugh Woodin in the 1980s. It is a means of constructing generic elementary embeddings and can be applied to produce a variety of useful forcing effects. Hugh Woodin is a leading figure in modern set theory, having made many deep and lasting contributions to the field, in particular to descriptive set theory and large cardinals. This book is the first detailed treatment of his method of the stationary tower that is generally accessible to graduate students in mathematical logic. By giving complete proofs of all the main theorems and discussing them in context, it is intended that the book will become the standard reference on the stationary tower and its applications to descriptive set theory. The first two chapters are taken from a graduate course Woodin taught at Berkeley. The concluding theorem in the course was that large cardinals imply that all sets of reals in the smallest model of set theory (without choice) containing the reals are Lebesgue measurable. Additional sections include a proof (using the stationary tower) of Woodin's theorem that, with large cardinals, the Continuum Hypothesis settles all questions of the same complexity as well as some of Woodin's applications of the stationary tower to the studies of absoluteness and determinacy. The 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
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
The stationary tower is an important method in modern set theory, invented by Hugh Woodin in the 1980s. It is a means of constructing generic elementary embeddings and can be applied to produce a variety of useful forcing effects. Hugh Woodin is a leading figure in modern set theory, having made many deep and lasting contributions to the field, in particular to descriptive set theory and large cardinals. This book is the first detailed treatment of his method of the stationary tower that is generally accessible to graduate students in mathematical logic. By giving complete proofs of all the main theorems and discussing them in context, it is intended that the book will become the standard reference on the stationary tower and its applications to descriptive set theory. The first two chapters are taken from a graduate course Woodin taught at Berkeley. The concluding theorem in the course was that large cardinals imply that all sets of reals in the smallest model of set theory (without choice) containing the reals are Lebesgue measurable. Additional sections include a proof (using the stationary tower) of Woodin's theorem that, with large cardinals, the Continuum Hypothesis settles all questions of the same complexity as well as some of Woodin's applications of the stationary tower to the studies of absoluteness and determinacy. The 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
Supercompact cardinals, sets of reals, and weakly homogeneous trees by
W. H Woodin(
)
1 edition published in 1988 in Undetermined and held by 1 WorldCat member library worldwide
It is shown that if there exists a supercompact cardinal then every set of reals, which is an element of [Note: See the image of page 6587 for this formatted text] L(R), is the projection of a weakly homogeneous tree. As a consequence of this theorem and recent work of Martin and Steel [Martin, D. A. & Steel, J. R. (1988) Proc. Natl. Acad. Sci. USA 85, 65826586], it follows that (if there is a supercompact cardinal) every set of reals in [Note: See the image of page 6587 for this formatted text] L(R) is determined
1 edition published in 1988 in Undetermined and held by 1 WorldCat member library worldwide
It is shown that if there exists a supercompact cardinal then every set of reals, which is an element of [Note: See the image of page 6587 for this formatted text] L(R), is the projection of a weakly homogeneous tree. As a consequence of this theorem and recent work of Martin and Steel [Martin, D. A. & Steel, J. R. (1988) Proc. Natl. Acad. Sci. USA 85, 65826586], it follows that (if there is a supercompact cardinal) every set of reals in [Note: See the image of page 6587 for this formatted text] L(R) is determined
Slicing the truth : on the computable and reverse mathematics of combinatorial principles by
Denis Roman Hirschfeldt(
Book
)
1 edition published in 2015 in English and held by 1 WorldCat member library 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
1 edition published in 2015 in English and held by 1 WorldCat member library 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
[Letter to stockholders in response to a circular letter sent to all stockholders attacking the management and organizers
of The Brill Corporation] by
W. H Woodin(
Book
)
1 edition published in 1931 in English and held by 1 WorldCat member library worldwide
1 edition published in 1931 in English and held by 1 WorldCat member library worldwide
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
1 edition published in 1995 in English and held by 0 WorldCat member libraries worldwide
Infinity and truth(
)
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
Section I. Invited lectures  section II. Special session
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
Section I. Invited lectures  section II. Special session
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Related Identities
 Chong, C.T (ChiTat) 1949 Editor
 Slaman, T. A. (Theodore Allen) 1954 Editor
 Feng, Qi 1955 Editor
 Dales, H. G. (Harold G.) 1944 Author
 Yang, Yue 1964 Editor
 Todorcevic, Stevo Author
 Heller, Michał Author Editor
 Judah, H. (Haim) Author Editor
 Just, W. (Winfried) Editor
 Mathematical Sciences Research Institute (Berkeley, Calif.) Editor
Useful Links
Associated Subjects
Axiomatic set theory Axioms Baire classes Borel sets Cardinal numbers Combinatorial analysis Forcing (Model theory) Independence (Mathematics) Infinite Logic, Symbolic and mathematical Mathematics MathematicsPhilosophy Model theory Ordered fields 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 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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