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A Model–Theoretic Approach to Proof Theory

Record Type:	Language materials, printed : Monograph/item
Title/Author:	A Model–Theoretic Approach to Proof Theory/ by Henryk Kotlarski ; edited by Zofia Adamowicz, Teresa Bigorajska, Konrad Zdanowski.
Author:	Kotlarski, Henryk.
other author:	Adamowicz, Zofia.
Description:	XVIII, 109 p. 53 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Logic. -
Online resource:	https://doi.org/10.1007/978-3-030-28921-8
ISBN:	9783030289218

A Model–Theoretic Approach to Proof Theory
Kotlarski, Henryk.

A Model–Theoretic Approach to Proof Theory[electronic resource] /by Henryk Kotlarski ; edited by Zofia Adamowicz, Teresa Bigorajska, Konrad Zdanowski. - 1st ed. 2019. - XVIII, 109 p. 53 illus., 1 illus. in color.online resource. - Trends in Logic, Studia Logica Library,511572-6126 ;. - Trends in Logic, Studia Logica Library,42.

Chapter 1. Some combinatorics -- Chapter 2. Some model theory -- Chapter 3. Incompleteness -- Chapter 4. Transﬁnite induction -- Chapter 5. Satisfaction classes.

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 Gödel'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 last chapter considers nonstandard satisfaction classes. It presents some of the classical theorems related to them. In particular, it covers the results by S. Smith on definability in the language with a satisfaction class and on models without a satisfaction class. Overall, the book's content lies on the border between combinatorics, proof theory, and model theory of arithmetic. It offers readers a distinctive approach towards independence results by model-theoretic methods.

ISBN: 9783030289218

Standard No.: 10.1007/978-3-030-28921-8doiSubjects--Topical Terms:

558909
Logic.

LC Class. No.: BC1-199

Dewey Class. No.: 160

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