Titlebook: Advances in Proof Theory; Reinhard Kahle,Thomas Strahm,Thomas Studer Book 2016 Springer International Publishing Switzerland 2016 construc

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Towards Optimal Sampling in?Diffusion?MRI to recent works of J?ger and Probst [.] and Ranzi and Strahm [.] on iterated stratified inductive definitions, but their theories have full, complete induction as basis, whereas ours have only a weak, ramified form of numerical induction at bottom.

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2297-0576 is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reason978-3-319-80513-9978-3-319-29198-7Series ISSN 2297-0576 Series E-ISSN 2297-0584

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Serge Vasylechko,Onur Afacan,Sila Kurugolhe infinitary propositional counterpart . of the Barcan Formula. We introduce a generalization of standard Kripke semantics, and prove that . is sound and complete with respect to it. By the same proof strategy, we show that the stronger system ., allowing . sequents, axiomatizes ., although it provably does not admit cut-elimination.

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Book 2016 discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard J?ger, who has been instrumental

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