Gabriel Debs's Books

Borel Liftings of Borel Sets: Some Decidable and Undecidable Statements

Some Decidable and Undecidable Statements

By: Gabriel Debs,Jean Saint Raymond

Write a review Read reviews Take a Quiz Solve Book Puzzle

Borel Liftings of Borel Sets: Some Decidable and Undecidable Statements

Some Decidable and Undecidable Statements

By: Gabriel Debs,Jean Saint Raymond

One of the aims of this work is to investigate some natural properties of Borel sets which are undecidable in $ZFC$. The authors' starting point is the following elementary, though non-trivial result: Consider $X \subset 2omega\times2omega$, set $Y=\pi(X)$, where $\pi$ denotes the canonical projection of $2omega\times2omega$ onto the first factor, and suppose that $(\star)$: Any compact subset of $Y$ is the projection of some compact subset of $X$. If moreover $X$ is $\mathbf{\Pi 0 2$ then $(\star\star)$: The restriction of $\pi$ to some relatively closed subset of $X$ is perfect onto $Y$ it follows that in the present case $Y$ is also $\mathbf{\Pi 0 2$. Notice that the reverse implication $(\star\star)\Rightarrow(\star)$ holds trivially for any $X$ and $Y$. But the implication $(\star)\Rightarrow (\star\star)$ for an arbitrary Borel set $X \subset 2omega\times2omega$ is equivalent to the statement $\forall \alpha\in \omegaomega, \, \aleph 1$ is inaccessible in $L(\alpha)$. More precisely The authors prove that the validity of $(\star)\Rightarrow(\star\star)$ for all $X \in \varSigma0 {1+\xi+1 $, is equivalent to $\aleph \xi \aleph 1$. $ZFC$, derive from $(\star)$ the weaker conclusion that $Y$ is also Borel and of the same Baire class as $X$. This last result solves an old problem about compact covering mappings. In fact these results are closely related to the following general boundedness principle Lift$(X, Y)$: If any compact subset of $Y$ admits a continuous lifting in $X$, then $Y$ admits a continuous lifting in $X$, where by a lifting of $Z\subset \pi(X)$ in $X$ we mean a mapping on $Z$ whose graph is contained in $X$. The main result of this work will give the exact set theoretical strength of this principle depending on the descriptive complexity of $X$ and $Y$. The authors also prove a similar result for a variation of Lift$(X, Y)$ in which continuous liftings are replaced by Borel liftings, and which answers a question of H. Friedman. Among other applications the authors obtain a complete solution to a problem which goes back to Lusin concerning the existence of $\mathbf{\Pi 1 1$ sets with all constituents in some given class $\mathbf{\Gamma $ of Borel sets, improving earlier results by J. Stern and R. Sami. Borel sets (in $ZFC$) of a new type, involving a large amount of abstract algebra. This representation was initially developed for the purposes of this proof, but has several other applications.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

134

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839713

ISBN 13

9780821839713

Necessary Secrets: National Security, the Media, and the Rule of Law

By: Gabriel Schoenfeld

Write a review Read reviews Take a Quiz Solve Book Puzzle

Necessary Secrets: National Security, the Media, and the Rule of Law

By: Gabriel Schoenfeld

An intensely controversial scrutiny of American democracy's fundamental tension between the competing imperatives of security and openness.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

323

Publisher

W. W. Norton & Company

Published Date

ISBN 10

0393339939

ISBN 13

9780393339932

Information-Centric Networks

A New Paradigm for the Internet

By: Gabriel M. de Brito,Pedro B. Velloso,Igor M. Moraes

Write a review Read reviews Take a Quiz Solve Book Puzzle

Information-Centric Networks

A New Paradigm for the Internet

By: Gabriel M. de Brito,Pedro B. Velloso,Igor M. Moraes

Since its inception, the Internet has evolved from a textual information system towards a multimedia information system, in which data, services and applications are consumed as content. Today, however, the main problem faced is that applications are now content-oriented but the protocol stack remains the same, based on the content location. Thus, it is clear that the Internet’s current architecture must change. This new architecture should take into account aspects to improve content location and delivery efficiency and also content availability. Fulfilling these requirements is the main goal of information-centric networks (ICNs). ICN is a new communication paradigm to increase the efficiency of content delivery and also content availability. In this new concept, the network infrastructure actively contributes to content caching and distribution. This book presents the basic concepts of ICNs, describes the main architecture proposals for these networks, and discusses the main challenges to their development. Information Centric-Networks looks at the current challenges for this concept, including: naming, routing and caching on the network-core elements, several aspects of content security, user privacy, and practical issues in implementing ICNs. Contents 1. Content Distribution on the Internet. 2. Information-Centric Networks. 3. Main ICN Architectures. 4. Challenges. 5. Practical Issues. About the Authors Gabriel M. Brito is an Engineer at Petrobras in Brazil and studying for a Master’s degree at the Universidade Federal Fluminense in Brazil. Pedro Braconnot Velloso is an Associate Professor in the Department of Computer Science at the Universidade Federal Fluminense (UFF), Brazil. He worked for Bell Labs France as a research engineer from 2009 to 2011. Igor M. Moraes is an Associate Professor at the Universidade Federal Fluminense in Brazil.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

100

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118579895

ISBN 13

9781118579893

Through Streets Broad and Narrow

By: Gabriel Fielding

Write a review Read reviews Take a Quiz Solve Book Puzzle

Through Streets Broad and Narrow

By: Gabriel Fielding

In this sequel to the acclaimed In the Time of Greenbloom, John Blaydon "runs head on into the paradox of Ireland, attempts to solve it single-handed and gets his heart and most of his head broken in the process. The manner of his undoing is told in a series of brilliant pictures, evocative, authentic, macabre, or hilariously funny. . . . Mr. Fielding has written an original novel of vitality, wit, and compassionate insight."—Isabelle Mallet, New York Times Book Review "A powerful and beautifully written novel, "Streets" can either stand by itself or solidly in company with In the Time of Greenbloom. . . . [Fielding's] touch is as sure and controlled as his invention is unlimited, and the resultant work seems various and beautiful and new. The major objection to the book is not its ending, but that it ends. It is too good to give up, too vital and dynamic to leave."—Margaret Marble, Los Angeles Times "A prismatic study of a finely gifted man in the elaborate tangles of his growth in a complex and wonderfully drawn environment."—Newsweek "Fielding writes a torrential prose, and his imagist phrases, fabulous incidents, antic characters and peripheral violence whip the story forward."—Time

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

356

Publisher

University of Chicago Press

Published Date

ISBN 10

0226248445

ISBN 13

9780226248448

The Next Shift

The Fall of Industry and the Rise of Health Care in Rust Belt America

By: Gabriel Winant

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Next Shift

The Fall of Industry and the Rise of Health Care in Rust Belt America

By: Gabriel Winant

Men in hardhats were once the heart of America’s working class; now it is women in scrubs. What does this shift portend for our future? Pittsburgh was once synonymous with steel. But today most of its mills are gone. Like so many places across the United States, a city that was a center of blue-collar manufacturing is now dominated by the service economy—particularly health care, which employs more Americans than any other industry. Gabriel Winant takes us inside the Rust Belt to show how America’s cities have weathered new economic realities. In Pittsburgh’s neighborhoods, he finds that a new working class has emerged in the wake of deindustrialization. As steelworkers and their families grew older, they required more health care. Even as the industrial economy contracted sharply, the care economy thrived. Hospitals and nursing homes went on hiring sprees. But many care jobs bear little resemblance to the manufacturing work the city lost. Unlike their blue-collar predecessors, home health aides and hospital staff work unpredictable hours for low pay. And the new working class disproportionately comprises women and people of color. Today health care workers are on the front lines of our most pressing crises, yet we have been slow to appreciate that they are the face of our twenty-first-century workforce. The Next Shift offers unique insights into how we got here and what could happen next. If health care employees, along with other essential workers, can translate the increasing recognition of their economic value into political power, they may become a major force in the twenty-first century.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

369

Publisher

Harvard University Press

Published Date

ISBN 10

0674238095

ISBN 13

9780674238091

America in the United States and the United States in America

A Philosophical Essay

By: Gabriel Moran

Write a review Read reviews Take a Quiz Solve Book Puzzle

America in the United States and the United States in America

A Philosophical Essay

By: Gabriel Moran

America is five hundred years old; the United States is less than half that age. The term America was coined in 1507 to refer to a continent and a dream of a new world. People in the United States, especially government leaders, have a serious problem of regularly speaking as if their country were America. Author Gabriel Moran reflects on the use of the word America in the United States from its beginning to the present. He cites numerous examples to show the importance of distinguishing between the United States and America. The result is a different way of perceiving and understanding the history of the United States. This book is especially relevant to the current political division within the United States and some of the missteps in its foreign policy. The failure to consistently distinguish between the nation of the United States and the continent and dream America underlies nearly every political, cultural and economic problem that the country faces.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

371

Publisher

iUniverse

Published Date

ISBN 10

1532044461

ISBN 13

9781532044465

Scipio Africanus

Rome's Greatest General

By: Richard A. Gabriel

Write a review Read reviews Take a Quiz Solve Book Puzzle

Scipio Africanus

Rome's Greatest General

By: Richard A. Gabriel

The world often misunderstands its greatest men while neglecting others entirely. Scipio Africanus, surely the greatest general that Rome produced, suffered both these fates. Today scholars celebrate the importance of Hannibal, even though Scipio defeated the legendary general in the Second Punic War and was the central military figure of his time. In this scholarly and heretofore unmatched military biography of the distinguished Roman soldier, Richard A. Gabriel establishes Scipio's rightful place in military history as the greater of the two generals. Before Scipio, few Romans would have dreamed of empire, and Scipio himself would have regarded such an ambition as a danger to his beloved republic. And yet, paradoxically, Scipio's victories in Spain and Africa enabled Rome to consolidate its hold over Italy and become the dominant power in the western Mediterranean, virtually ensuring a later confrontation with the Greco-Macedonian kingdoms to the east as well as the empire's expansion into North Africa and the Levant. The Roman imperium was being born, and it was Scipio who had sired it. Gabriel draws upon ancient texts, including those from Livy, Polybius, Diodorus, Silius Italicus, and others, as primary sources and examines all additional material available to the modern scholar in French, German, English, and Italian. His book offers a complete bibliography of all extant sources regarding Scipio's life. The result is a rich, detailed, and contextual treatment of the life and career of Scipio Africanus, one of Rome's greatest generals, if not the greatest of them all.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

452

Publisher

Potomac Books, Inc.

Published Date

ISBN 10

1597979988

ISBN 13

9781597979986

Living Nonviolently

Language for Resisting Violence

By: Gabriel Moran

Write a review Read reviews Take a Quiz Solve Book Puzzle

Living Nonviolently

Language for Resisting Violence

By: Gabriel Moran

Living Nonviolently: Language for Resisting Violence proposes distinctions of language that effectively address issues of force, power, aggressiveness, violence and war. No other book provides such a consistent language for living nonviolently through examples drawn from nonhuman animals, human infancy, personal transactions, domestic politics, and international conflicts.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

218

Publisher

Lexington Books

Published Date

ISBN 10

0739150456

ISBN 13

9780739150450

Triumph of Conservatism

By: Gabriel Kolko

Write a review Read reviews Take a Quiz Solve Book Puzzle

Triumph of Conservatism

By: Gabriel Kolko

A radically new interpretation of the Progressive Era which argues that business leaders, and not the reformers, inspired the era’s legislation regarding business.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

362

Publisher

Simon and Schuster

Published Date

ISBN 10

1439118728

ISBN 13

9781439118726

Main Currents in Modern American History

By: Gabriel Kolko

Write a review Read reviews Take a Quiz Solve Book Puzzle

Main Currents in Modern American History

By: Gabriel Kolko

A major reinterpretation of the nature and uses of power and its institutions in the twentieth century, with a new epilogue"--Cover.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

484

Publisher

Pantheon

Published Date

ISBN 10

0394725123

ISBN 13

9780394725123

Borel Liftings of Borel Sets

Some Decidable and Undecidable Statements

By: Gabriel Debs

Write a review Read reviews Take a Quiz Solve Book Puzzle

Borel Liftings of Borel Sets

Some Decidable and Undecidable Statements

By: Gabriel Debs

One of the aims of this work is to investigate some natural properties of Borel sets which are undecidable in $ZFC$. The authors' starting point is the following elementary, though non-trivial result: Consider $X \subset 2omega\times2omega$, set $Y=\pi(X)$, where $\pi$ denotes the canonical projection of $2omega\times2omega$ onto the first factor, and suppose that $(\star)$ : ''Any compact subset of $Y$ is the projection of some compact subset of $X$''. If moreover $X$ is $\mathbf{\Pi 0 2$ then $(\star\star)$: ''The restriction of $\pi$ to some relatively closed subset of $X$ is perfect onto $Y$'' it follows that in the present case $Y$ is also $\mathbf{\Pi 0 2$. Notice that the reverse implication $(\star\star)\Rightarrow(\star)$ holds trivially for any $X$ and $Y$. But the implication $(\star)\Rightarrow (\star\star)$ for an arbitrary Borel set $X \subset 2omega\times2omega$ is equivalent to the statement ''$\forall \alpha\in \omegaomega, \,\aleph 1$ is inaccessible in $L(\alpha)$''. More precisely The authors prove that the validity of $(\star)\Rightarrow(\star\star)$ for all $X \in \varSigma0 {1+\xi+1 $, is equivalent to ''$\aleph \xi lifting of $Z\subset \pi(X)$ in $X$ we mean a mapping on $Z$ whose graph is contained in $X$. The main result of this work will give the exact set theoretical strength of this principle depending on the descriptive complexity of $X$ and $Y$. The authors also prove a similar result for a variation of Lift$(X, Y)$ in which ''continuous liftings'' are replaced by ''Borel liftings'', and which answers a question of H. Friedman. Among other applications the authors obtain a complete solution to a problem which goes back to Lusin concerning the existence of $\mathbf{\Pi 1 1$ sets with all constituents in some given class $\mathbf{\Gamma $ of Borel sets, improving earlier results by J. Stern and R. Sami. The proof of the main result will rely on a nontrivial representation of Borel sets (in $ZFC$) of a new type, involving a large amount of ''abstract algebra''. This representation was initially developed for the purposes of this proof, but has several other applications.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

142

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821866176

ISBN 13

9780821866177

Book's by Gabriel Debs

Borel Liftings of Borel Sets: Some Decidable and Undecidable Statements

Borel Liftings of Borel Sets: Some Decidable and Undecidable Statements

Necessary Secrets: National Security, the Media, and the Rule of Law

Necessary Secrets: National Security, the Media, and the Rule of Law

Information-Centric Networks

Information-Centric Networks

Through Streets Broad and Narrow

Through Streets Broad and Narrow

The Next Shift

The Next Shift

America in the United States and the United States in America

America in the United States and the United States in America

Scipio Africanus

Scipio Africanus

Living Nonviolently

Living Nonviolently

Triumph of Conservatism

Triumph of Conservatism

Main Currents in Modern American History

Main Currents in Modern American History

Borel Liftings of Borel Sets

Borel Liftings of Borel Sets

Username

Password

Username

Password

Password again

Birthday

Email