| 期刊全稱 | A Model–Theoretic Approach to Proof Theory | | 影響因子2023 | Henryk Kotlarski,Zofia Adamowicz,Teresa Bigorajska | | 視頻video | http://file.papertrans.cn/142/141444/141444.mp4 | | 發(fā)行地址 | Details ordinal combinatorics of large sets tailored for independence results.Presents various proofs of G?del incompleteness theorems.Offers an approach towards independence results by model-theoreti | | 學(xué)科分類(lèi) | Trends in Logic | | 圖書(shū)封面 |  | | 影響因子 | .This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results. It uses model theoretic and combinatorial methods to obtain results in proof theory, such as incompleteness theorems or a description of the provably total functions of a theory..In the first chapter, the authors first discusses ordinal combinatorics of finite sets in the style of Ketonen and Solovay. This provides a background for an analysis of subsystems of Peano Arithmetic as well as for combinatorial independence results. Next, the volume examines a variety of proofs of G?del‘s incompleteness theorems. The presented proofs differ strongly in nature. They show various aspects of incompleteness phenomena. In additon, coverage introduces some classical methods like the arithmetized completeness theorem, satisfaction predicates or partial satisfaction classes. It also applies them in many contexts.?.The fourth chapter defines the method of indicators for obtaining independence results. It shows what amount of transfinite induction we have in fragments of Peano arithmetic. Then, it uses?combinatorics of large sets of the first chapter to show independence results. The | | Pindex | Book 2019 |
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