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Subsystems of Second Order Arithmetic
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  • Cited by 95
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Carlucci, Lorenzo 2018. A weak variant of Hindman’s Theorem stronger than Hilbert’s Theorem. Archive for Mathematical Logic, Vol. 57, Issue. 3-4, p. 381.

    Arai, Toshiyasu 2018. Derivatives of normal functions and $$\omega $$ ω -models. Archive for Mathematical Logic, Vol. 57, Issue. 5-6, p. 649.

    Schindler, Thomas 2018. Some Notes on Truths and Comprehension. Journal of Philosophical Logic, Vol. 47, Issue. 3, p. 449.

    Sanders, Sam 2018. Sailing Routes in the World of Computation. Vol. 10936, Issue. , p. 365.

    Towsner, Henry 2018. Epsilon substitution for $$\textit{ID}_1$$ ID 1 via cut-elimination. Archive for Mathematical Logic, Vol. 57, Issue. 5-6, p. 497.

    Avron, Arnon and Cohen, Liron 2018. Logical Foundations of Computer Science. Vol. 10703, Issue. , p. 37.

    Eastaugh, Benedict 2018. Set Existence Principles and Closure Conditions: Unravelling the Standard View of Reverse Mathematics†. Philosophia Mathematica,

    Omata, Yasuhiko and Pelupessy, Florian 2018. Dickson’s lemma and weak Ramsey theory. Archive for Mathematical Logic,

    Miquey, Étienne 2018. A sequent calculus with dependent types for classical arithmetic. p. 720.

    Adjali, Omar and Ramdane-Cherif, Amar 2017. Knowledge Processing Using EKRL for Robotic Applications. International Journal of Cognitive Informatics and Natural Intelligence, Vol. 11, Issue. 4, p. 1.

    Hirst, Jeffry L. and Mummert, Carl 2017. Computability and Complexity. Vol. 10010, Issue. , p. 143.

    Dowek, Gilles 2017. Analyzing Individual Proofs as the Basis of Interoperability between Proof Systems. Electronic Proceedings in Theoretical Computer Science, Vol. 262, Issue. , p. 3.

    Hachtman, Sherwood 2017. Determinacy in third order arithmetic. Annals of Pure and Applied Logic, Vol. 168, Issue. 11, p. 2008.

    Patey, Ludovic 2017. The reverse mathematics of non-decreasing subsequences. Archive for Mathematical Logic, Vol. 56, Issue. 5-6, p. 491.

    FUCHINO, Sakaé 2017. A Reflection Principle As a Reverse-mathematical Fixed Point over the Base Theory ZFC. Annals of the Japan Association for Philosophy of Science, Vol. 25, Issue. 0, p. 67.

    WONG, Tin Lok 2017. Models of the Weak König Lemma. Annals of the Japan Association for Philosophy of Science, Vol. 25, Issue. 0, p. 25.

    Fujimoto, Kentaro 2017. Deflationism beyond arithmetic. Synthese,

    Jäger, Gerhard 2017. Feferman on Foundations. Vol. 13, Issue. , p. 253.

    Skrzypczak, Michał 2017. Developments in Language Theory. Vol. 10396, Issue. , p. 75.

    Harrington, Leo Shore, Richard A. and Slaman, Theodore A. 2017. Computability and Complexity. Vol. 10010, Issue. , p. 455.


Book description

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.

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