Titlebook: Axiomatic Thinking I; Fernando Ferreira,Reinhard Kahle,Giovanni Sommarug Book 2022 Springer Nature Switzerland AG 2022 mathematical logic.

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The Two Sides of Modern Axiomatics: Dedekind and Peano, Hilbert and Bourbakiructure of a theory, and 2. the conceptual-mathematical side, often linked to the establishment of new interconnections in mathematics, or ‘deeper’ ways of grounding some results. We explore this question, first by offering some classic examples in papers due to Hilbert and Bourbaki (and Hausdorff),

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Notes for a Seminar in Axiomatic Reasoninguided by the passions and expertise of our students-my co-teachers (Amartya Sen and Eric Maskin) and I were able to shape our seminar course on .. I want to thank Giovanni Sommaruga for inviting me to include these notes in this volume, suggesting that I edit them slightly so that they offer a “many

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s, physicists and computer scientists with an interest in fo.In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert‘s axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics,

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https://doi.org/10.1007/978-981-10-0719-4ctual intuition is no longer needed for providing the objects of mathematical theories and the requirement of truth is replaced by the requirement of ..This approach has immediate consequence of an ontological nature, i.e. regarding the . of mathematical entities (Is consistency a sufficient condition for existence in mathematics?).

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The Semantic Function of the Axiomatic Methodctual intuition is no longer needed for providing the objects of mathematical theories and the requirement of truth is replaced by the requirement of ..This approach has immediate consequence of an ontological nature, i.e. regarding the . of mathematical entities (Is consistency a sufficient condition for existence in mathematics?).