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Subsystems of Second Order Arithmetic (Perspectives in Logic)

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Subsystems of Second Order Arithmetic (Perspectives in Logic)

4.85 25,346 ratings · 2,385 reviews
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Overview: Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic. Additional results are presented in an appendix.

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Book details & editions

ISBN
8619579
Publication date
December 11, 1998
Language
Eng
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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Stephen G. Simpson
About the Author
Stephen G. Simpson
13,152 Followers

Stephen G. Simpson is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Stephen G. Simpson can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Edward Perez
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. 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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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Absolutely brilliant. 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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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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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.
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Daniel Campbell September 26, 2024
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Jessica Ramirez
Jessica Ramirez September 03, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Lisa Ramirez
Lisa Ramirez April 26, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Mary Lopez
Mary Lopez July 15, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Mark Flores
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
John Adams
John Adams March 10, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Thomas  Davis
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Daniel Moore
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Eric Wright
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Donald Rivera
Donald Rivera October 30, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Joshua Evans
Joshua Evans September 19, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Christopher Lee
Christopher Lee April 12, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
James Johnson
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Ryan Wilson
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Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
William Lee
William Lee August 24, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
David Thompson
David Thompson May 18, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Eric Martinez
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Lisa Campbell
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Melissa Martinez
Melissa Martinez October 14, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
James Carter
James Carter January 25, 2024
Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. A fair 3 stars.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Rebecca Green
Rebecca Green October 04, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Charles Brown
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A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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