The Godel Operation
The Godel Operation

Author: James L. Cambias

Publisher: Baen Books

Published: 2021-05-04

Total Pages: 345

ISBN-13: 1625798083

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Science fiction at its sense-of-wonder best. A wild chase through the billion worlds of the Tenth Millennium in search of a mythical weapon that could save civilization—or doom it! A DROID AND HIS BOY, ON A SEARCH FOR A LEGENDARY WEAPON Daslakh is an AI with a problem. Its favorite human, a young man named Zee, is in love with a woman who never existed—and he will scour the Solar System to find her. But in the Tenth Millennium, a billion worlds circle the Sun—everything from terraformed planets to artificial habitats, home to a quadrillion beings. Daslakh’s nicely settled life gets more complicated when Zee helps a woman named Adya escape a gang of crooks. This gets the pair caught up in the hunt for the Godel Trigger, a legendary weapon left over from an ancient war between humans and machines—which could spell the end of civilization. In their search, they face a criminal cat and her henchmen, a paranoid supermind with a giant laser, the greatest thief in history, and a woman who might actually be Zee’s lost love. It’s up to Daslakh to save civilization, keep Zee’s love life on the right track—and make sure that nobody discovers the real secret of the Godel Trigger. At the publisher's request, this title is sold without DRM (Digital Rights Management). Praise for the work of James L. Cambias: “Beautifully written, with a story that captures the imagination the way SF should.”—Booklist, starred review “An engaging nail-biter that is exciting, fun and a satisfying read.”—The Qwillery '“An impressive debut by a gifted writer.”—Publishers Weekly, starred review “An exceptionally thoughtful, searching and intriguing debut.”—Kirkus, starred review “James Cambias will be one of the century's major names in hard science fiction.”—Robert J. Sawyer, Hugo Award–winning author of Red Planet Blues “Fast-paced, pure quill hard science fiction. . . . Cambias delivers adroit plot pivots that keep the suspense coming.”—Gregory Benford, Nebula Award-winning author of Timescape

Kurt Gödel and the Foundations of Mathematics
Kurt Gödel and the Foundations of Mathematics

Author: Matthias Baaz

Publisher: Cambridge University Press

Published: 2011-06-06

Total Pages: 541

ISBN-13: 1139498436

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This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

The Initiate
The Initiate

Author: James L. Cambias

Publisher: Baen Books

Published: 2020-02-04

Total Pages: 288

ISBN-13: 1625797532

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A SECRET ORDER OF SORCERERS RULES THE WORLD. ONE MAN HAS VOWED TO DESTROY THEM. It's their world. He's going to take it away from them. The Apkallu are masters of magic. Theirs is a secret tradition stretching back to the dawn of civilization. They rule the world from the shadows, using mind control and deadly monsters to eliminate any threat to their power. If they know your name, or have a trace of your blood, you can never defy them. Sam Arquero lost his family to a demon, and knew that nobody would believe the truth. An old man named Lucas offers him the chance to find out who is responsible, and bring down the Apkallu forever. All he has to do is join them . . . Under a new identity Sam learns the secrets of magic, infiltrates the Apkallu, and walks a razor's edge as he picks off their leaders while avoiding supernatural detectives on his trail. But Sam faces a greater threat: As he fights monsters, what is he becoming? At the publisher's request, this title is sold without DRM (Digital Rights Management). Praise for Arkad's World: “Far-flung adventure . . . Cambias offers up an entertaining coming-of-age novel filled with action and surprises. His aliens are suitably non-human in mannerisms, attitudes, and objectives, and his worldbuilding suggests a vast universe ready for further exploration. Readers . . . will find this hits the spot.”—Publishers Weekly “. . . a classic quest story, a well-paced series of encounters with different folk along the way, building momentum toward a final confrontation with Arkad's past. . . [with] a delicious twist to the end.”—ALA Booklist "Cambias has achieved a feat of world-building: an expansive, believable setting with fascinating aliens, compelling mysteries, and a rich sense of history."—Bookpage "Drop a teenage boy into a distant planet chock full of colorful aliens—with troubles all their own. Stir, flavor, apply heat. A tour de force in the field, and great, quick fun."—Gregory Benford Praise for the work of James L. Cambias: "Beautifully written, with a story that captures the imagination the way SF should."—Booklist, starred review “An engaging nail-biter that is exciting, fun and a satisfying read.” —The Qwillery "An impressive debut by a gifted writer."—Publishers Weekly, starred review "An exceptionally thoughtful, searching and intriguing debut."—Kirkus, starred review "James Cambias will be one of the century's major names in hard science fiction."—Robert J. Sawyer, Hugo Award–winning author of Red Planet Blues "Fast-paced, pure quill hard science fiction. . . . Cambias delivers adroit plot pivots that keep the suspense coming."—Gregory Benford, Nebula Award-winning author of Timescape

Arkad's World
Arkad's World

Author: James L. Cambias

Publisher: Baen

Published: 2019-12-31

Total Pages: 0

ISBN-13: 9781982124328

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ADVENTURE AND EXCITEMENT ON AN ALIEN WORLD. Packed with exotic world-building and amazing characters, Arkad's World is a rollicking adventure story about growing up and the things we share that make us human, from celebrated author James L. Cambias. CROSS A MAD PLANET FOR TREASURE - AND FREEDOM Young Arkad is the only human on a distant world, on his own among beings from across the Galaxy. His struggle to survive on the lawless streets of an alien city is disrupted by the arrival of three humans: an eccentric historian named Jacob, a superhuman cyborg girl called Baichi, and a mysterious ex-spy known as Ree. They seek a priceless treasure that might free Earth from alien domination. Arkad risks everything to join them on an incredible quest halfway across the planet. With his help, they cross the fantastic landscape, battling pirates, mercenaries, bizarre creatures, vicious bandits, and the harsh environment. But the deadliest danger comes from treachery and betrayal within the group, as dark secrets and hidden loyalties come to light. Praise for Arkad's World: “Far-flung adventure . . . Cambias offers up an entertaining coming-of-age novel filled with action and surprises. His aliens are suitably non-human in mannerisms, attitudes, and objectives, and his worldbuilding suggests a vast universe ready for further exploration. Readers . . . will find this hits the spot.”—Publishers Weekly “. . . a classic quest story, a well-paced series of encounters with different folk along the way, building momentum toward a final confrontation with Arkad's past . . . [with] a delicious twist to the end.”—ALA Booklist "Cambias has achieved a feat of world-building: an expansive, believable setting with fascinating aliens, compelling mysteries, and a rich sense of history."—Bookpage "Drop a teenage boy into a distant planet chock full of colorful aliens—with troubles all their own. Stir, flavor, apply heat. A tour de force in the field, and great, quick fun."—Gregory Benford Praise for the work of James L. Cambias: "Beautifully written, with a story that captures the imagination the way SF should."—Booklist, Starred Review “An engaging nail-biter that is exciting, fun and a satisfying read.” —The Qwillery ''An impressive debut by a gifted writer.''—Publishers Weekly, Starred Review ''An exceptionally thoughtful, searching and intriguing debut.''—Kirkus, Starred Review "James Cambias will be one of the century's major names in hard science fiction.''—Robert J. Sawyer, Hugo Award-winning author of Red Planet Blues "Fast-paced, pure quill hard science fiction. . . . Cambias delivers adroit plot pivots that keep the suspense coming.''—Gregory Benford, Nebula Award-winning author of Timescape

Gödel's Disjunction
Gödel's Disjunction

Author: Leon Horsten

Publisher: Oxford University Press

Published: 2016-09-09

Total Pages: 288

ISBN-13: 0191077682

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The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.

An Introduction to Gödel's Theorems
An Introduction to Gödel's Theorems

Author: Peter Smith

Publisher: Cambridge University Press

Published: 2007-07-26

Total Pages: 376

ISBN-13: 1139465937

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In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

Set Theory
Set Theory

Author: Thomas Jech

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 642

ISBN-13: 3662224003

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The main body of this book consists of 106 numbered theorems and a dozen of examples of models of set theory. A large number of additional results is given in the exercises, which are scattered throughout the text. Most exer cises are provided with an outline of proof in square brackets [ ], and the more difficult ones are indicated by an asterisk. I am greatly indebted to all those mathematicians, too numerous to men tion by name, who in their letters, preprints, handwritten notes, lectures, seminars, and many conversations over the past decade shared with me their insight into this exciting subject. XI CONTENTS Preface xi PART I SETS Chapter 1 AXIOMATIC SET THEORY I. Axioms of Set Theory I 2. Ordinal Numbers 12 3. Cardinal Numbers 22 4. Real Numbers 29 5. The Axiom of Choice 38 6. Cardinal Arithmetic 42 7. Filters and Ideals. Closed Unbounded Sets 52 8. Singular Cardinals 61 9. The Axiom of Regularity 70 Appendix: Bernays-Godel Axiomatic Set Theory 76 Chapter 2 TRANSITIVE MODELS OF SET THEORY 10. Models of Set Theory 78 II. Transitive Models of ZF 87 12. Constructible Sets 99 13. Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis 108 14. The In Hierarchy of Classes, Relations, and Functions 114 15. Relative Constructibility and Ordinal Definability 126 PART II MORE SETS Chapter 3 FORCING AND GENERIC MODELS 16. Generic Models 137 17. Complete Boolean Algebras 144 18.