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Higher Recursion Theory (Perspectives in Mathematical Logic)

Higher Recursion Theory (Perspectives in Mathematical Logic)

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4.85
91,803 ratings · 6,312 reviews
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Higher Recursion Theory (Perspectives in Mathematical Logic)

Higher Recursion Theory (Perspectives in Mathematical Logic)

4.85 91,803 ratings · 6,312 reviews
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Overview: Hyperarithmetic theory is the first step beyond classical recursion theory. It is the primary source of ideas and examples in higher recursion theory. It is also a crossroad for several areas of mathematical logic: in set theory it is an initial segment of Godel's L; in model theory, the least admissible set after; in descriptive set theory, the setting for effective arguments. In this book, hyperarithmetic theory is developed at length and used to lift classical recursion theory from integers to recursive ordinals (metarecursion). Two further liftings are then made, first ordinals ( -recursion) and then to sets (E-recursion). Techniques such as finite and infinite injury, forcing and fine structure and extended and combined Dynamic and syntactical methods are contrasted. Several notions of reducibility and computation are compared. Post's problem is answere affirmatively in all three settings. This long-awaited volume of the -series will be a "Must" for all working in the field.

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Book details & editions

ISBN
3669929
Publication date
1990
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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Gerald E. Sacks
About the Author
Gerald E. Sacks
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Gerald E. Sacks is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Gerald E. Sacks enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Edward  Davis
Edward Davis August 05, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Michael Campbell August 04, 2024
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Susan Sanchez May 26, 2024
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Carol Phillips
Carol Phillips July 31, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Ryan Scott
Ryan Scott July 07, 2024
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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Brian Rivera August 21, 2024
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Christopher Mitchell September 27, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Robert Sanchez March 28, 2025
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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John Hall October 04, 2025
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Anthony Rodriguez March 29, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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Margaret Wilson October 17, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
James Walker
James Walker May 01, 2024
A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
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Matthew Lewis December 09, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Karen Hill August 18, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
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Susan Baker September 21, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Dorothy Wright
Dorothy Wright November 13, 2024
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Kevin Rivera
Kevin Rivera September 08, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Linda Hall October 23, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Ryan Scott September 11, 2025
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Matthew Davis November 29, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Margaret Nguyen August 29, 2024
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Michelle Thomas April 01, 2024
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Jessica Martin August 14, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Richard Phillips February 19, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Gary  Davis
Gary Davis July 14, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Joshua Roberts February 23, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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Charles Allen August 01, 2024
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Amanda Phillips December 14, 2024
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Richard Phillips January 29, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Barbara Miller October 20, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Karen Campbell May 24, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Cynthia Adams
Cynthia Adams March 09, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Steven Taylor October 12, 2024
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Jennifer Phillips May 08, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Susan Walker
Susan Walker March 27, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Donna Walker
Donna Walker January 01, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Ashley Garcia January 18, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Edward Anderson August 30, 2024
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Linda Mitchell
Linda Mitchell November 08, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Charles Allen
Charles Allen April 20, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Matthew Lopez
Matthew Lopez September 28, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Karen Torres
Karen Torres January 23, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Andrew Wright
Andrew Wright December 02, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Joshua Lopez
Joshua Lopez December 02, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Carol Lopez
Carol Lopez November 27, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Margaret Smith
Margaret Smith October 22, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
James Walker
James Walker October 02, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Stephanie Martin
Stephanie Martin January 21, 2024
Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
John Garcia
John Garcia January 09, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Nicholas Hill
Nicholas Hill March 29, 2025
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
Barbara Wright
Barbara Wright February 07, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Kenneth Miller
Kenneth Miller August 23, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Deborah King
Deborah King June 18, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
George  Davis
George Davis December 08, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Joshua Torres
Joshua Torres October 19, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Donna Walker
Donna Walker February 16, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Cynthia Baker
Cynthia Baker September 13, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Karen Nguyen
Karen Nguyen August 09, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Paul Young
Paul Young August 27, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Robert Phillips
Robert Phillips March 02, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Stephanie Turner
Stephanie Turner September 10, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Robert Roberts
Robert Roberts November 18, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Amanda Roberts
Amanda Roberts May 25, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Joshua Wilson
Joshua Wilson October 09, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Donna Flores
Donna Flores July 03, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Steven Sanchez
Steven Sanchez September 07, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Dorothy Turner
Dorothy Turner October 07, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Donna Martin
Donna Martin April 24, 2025
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Lisa Hall
Lisa Hall November 06, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Elizabeth King
Elizabeth King February 24, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Kimberly Ramirez
Kimberly Ramirez August 22, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Emily Phillips
Emily Phillips June 05, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Margaret Nguyen
Margaret Nguyen November 22, 2024
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
Emily Johnson
Emily Johnson November 13, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Edward Rivera
Edward Rivera December 08, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Donald Wright
Donald Wright May 04, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Robert Collins
Robert Collins November 29, 2024
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
Susan Phillips
Susan Phillips November 30, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Steven Evans
Steven Evans February 20, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Lisa Brown
Lisa Brown July 26, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Karen Walker
Karen Walker July 12, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Amanda Phillips
Amanda Phillips June 18, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Linda Torres
Linda Torres January 29, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Kevin Gomez
Kevin Gomez November 22, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Deborah Mitchell
Deborah Mitchell March 14, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
James Sanchez
James Sanchez November 25, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Kenneth Miller
Kenneth Miller July 06, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Kenneth Evans
Kenneth Evans January 05, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Joshua Moore
Joshua Moore August 26, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Charles Allen
Charles Allen October 22, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Susan Gonzalez
Susan Gonzalez May 16, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Jennifer Taylor
Jennifer Taylor February 18, 2024
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Jessica Thomas
Jessica Thomas May 10, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Thomas Nguyen
Thomas Nguyen July 11, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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