دانلود کتاب An Introduction to Proof Theory: Normalization, Cut-Elimination, and Consistency Proofs
by Paolo Mancosu, Sergio Galvan, Richard Zach
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عنوان فارسی: مقدمه ای بر تئوری اثبات: عادی سازی، حذف حذف و اثبات سازگاری |
دانلود کتاب
جزییات کتاب
half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various
applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The
proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy
of mathematics.