Titlebook: Computational Logic and Set Theory; Applying Formalized Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omod Textbook 2011 Springer-Verlag L

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https://doi.org/10.1007/978-3-642-88314-9o two parts: (i)?An account of the general syntax and overall structure of proofs acceptable to the verifier. (ii)?A?listing of the mechanisms actually chosen from the list of candidate inference mechanisms surveyed earlier in the book, for inclusion in the verifier’s initial endowment. The syntax u

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https://doi.org/10.1007/978-3-642-88314-9 development of a large-scale proof scenario. Ideally, to demonstrate that the verifier can certify the correctness of a substantial body of mathematical analysis, this proof scenario should have culminated in the proof of the celebrated . (whose statement is recalled at the end of this chapter). Th

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Endokrinologische Untersuchungen, . are derived: .These are easily proved using an elegant line of argument due to Gregory Chaitin. Then the somewhat more delicate line of argument leading to G?del’s two incompleteness theorems is considered: this more detailed discussion continues to emphasize the basic role of set theory..The cha

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Endokrinologische Untersuchungen,the transitive closure operation, transfinite induction, and then Zorn’s lemma. The proofs of a few basic facts concerning finite sets, including a finite induction principle, are also included..In preparation for the study of ordinals, the notion of reachability in a ‘big’ graph, which is a system

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978-1-4471-6018-2Springer-Verlag London Limited 2011

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Introduction,niz’s program, Boole’s algebra of propositions, Frege’s ., Peano’s axiomatization of arithmetic, Whitehead and Russell’s attempt at formalizing the whole corpus of mathematics, Descartes’ reduction of geometry to algebra, Cauchy’s formalization of continuity, Dedekind’s definition of the system of r