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Benedict Eastaugh
Ludwig Maximilians Universität, München
  1.  23
    Review of John Stillwell, Reverse Mathematics: Proofs From the Inside Out. [REVIEW]Benedict Eastaugh - 2020 - Philosophia Mathematica 28 (1):108-116.
    Review of John Stillwell, Reverse Mathematics: Proofs from the Inside Out. Princeton, NJ: Princeton University Press, 2018, pp. 200. ISBN 978-0-69-117717-5 (hbk), 978-0-69-119641-1 (pbk), 978-1-40-088903-7 (e-book).
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    Set Existence Principles and Closure Conditions: Unravelling the Standard View of Reverse Mathematics.Benedict Eastaugh - 2019 - Philosophia Mathematica 27 (2):153-176.
    It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset of (...)
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  3.  86
    Computational Reverse Mathematics and Foundational Analysis.Benedict Eastaugh - manuscript
    Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the (...)
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    Tarski.Benedict Eastaugh - 2017 - In Alex Malpass & Marianna Antonutti Marfori (eds.), The History of Philosophical and Formal Logic: From Aristotle to Tarski. London: Bloomsbury. pp. 293-313.
    Alfred Tarski was one of the greatest logicians of the twentieth century. His influence comes not merely through his own work but from the legion of students who pursued his projects, both in Poland and Berkeley. This chapter focuses on three key areas of Tarski's research, beginning with his groundbreaking studies of the concept of truth. Tarski's work led to the creation of the area of mathematical logic known as model theory and prefigured semantic approaches in the philosophy of language (...)
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  5.  59
    Review of Denis R. Hirschfeldt, Slicing the Truth: On the Computability Theoretic and Reverse Mathematical Analysis of Combinatorial Principles. [REVIEW]Benedict Eastaugh - 2017 - Studia Logica 105 (4):873-879.
    The present volume is an introduction to the use of tools from computability theory and reverse mathematics to study combinatorial principles, in particular Ramsey's theorem and special cases such as Ramsey's theorem for pairs. It would serve as an excellent textbook for graduate students who have completed a course on computability theory.
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