The Birth of Model Theory

The Birth of Model Theory
Author: Calixto Badesa
Publisher: Princeton University Press
Total Pages: 256
Release: 2009-01-10
Genre: Mathematics
ISBN: 1400826187

Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In The Birth of Model Theory, Calixto Badesa provides both the first sustained, book-length analysis of Löwenheim's proof and a detailed description of the theoretical framework--and, in particular, of the algebraic tradition--that made the theorem possible. Badesa's three main conclusions amount to a completely new interpretation of the proof, one that sharply contradicts the core of modern scholarship on the topic. First, Löwenheim did not use an infinitary language to prove his theorem; second, the functional interpretation of Löwenheim's normal form is anachronistic, and inappropriate for reconstructing the proof; and third, Löwenheim did not aim to prove the theorem's weakest version but the stronger version Skolem attributed to him. This book will be of considerable interest to historians of logic, logicians, philosophers of logic, and philosophers of mathematics.

The Birth of String Theory

The Birth of String Theory
Author: Andrea Cappelli
Publisher: Cambridge University Press
Total Pages: 663
Release: 2012-04-12
Genre: Science
ISBN: 0521197902

Explores the early stages of the development of string theory; essential reading for physicists, historians and philosophers of science.

The Birth of Model Theory

The Birth of Model Theory
Author: Calixto Badesa
Publisher:
Total Pages: 256
Release: 2009
Genre: Mathematics
ISBN:

Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In The Birth of Model Theory, Calixto Badesa provides both the first sustained, book-length analysis of Löwenheim's proof and a detailed description of the theoretical framework--and, in particular, of the algebraic tradition--that made the theorem possible. Badesa's three main conclusions amount to a completely new interpretation of the proof, one that sharply contradicts the core of modern scholarship on the topic. First, Löwenheim did not use an infinitary language to prove his theorem; second, the functional interpretation of Löwenheim's normal form is anachronistic, and inappropriate for reconstructing the proof; and third, Löwenheim did not aim to prove the theorem's weakest version but the stronger version Skolem attributed to him. This book will be of considerable interest to historians of logic, logicians, philosophers of logic, and philosophers of mathematics.

Elements of Finite Model Theory

Elements of Finite Model Theory
Author: Leonid Libkin
Publisher: Springer Science & Business Media
Total Pages: 320
Release: 2013-03-09
Genre: Mathematics
ISBN: 3662070030

Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.

Birth of a Theorem

Birth of a Theorem
Author: Cédric Villani
Publisher: Macmillan + ORM
Total Pages: 260
Release: 2015-04-14
Genre: Biography & Autobiography
ISBN: 0374710236

In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of aTheorem is Villani's own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career. But you don't have to understand nonlinear Landau damping to love Birth of aTheorem. It doesn't simplify or overexplain; rather, it invites readers into collaboration. Villani's diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to the dining-hall conversations at the world's greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker's whole life that propels discovery—and with Birth of aTheorem, Cédric Villani welcomes you into his.

Model Theory and the Philosophy of Mathematical Practice

Model Theory and the Philosophy of Mathematical Practice
Author: John T. Baldwin
Publisher: Cambridge University Press
Total Pages: 365
Release: 2018-01-25
Genre: Mathematics
ISBN: 1107189217

Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

Philosophy and Model Theory

Philosophy and Model Theory
Author: Tim Button
Publisher: Oxford University Press
Total Pages: 534
Release: 2018
Genre: Mathematics
ISBN: 0198790392

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.

25 Years of Model Checking

25 Years of Model Checking
Author: Orna Grumberg
Publisher: Springer Science & Business Media
Total Pages: 238
Release: 2008-06-17
Genre: Computers
ISBN: 3540698493

This Festschrift volume, published in celebration of the 25th Anniversary of Model Checking, features papers based on talks at the symposium "25 Years of Model Checking", 25MC, which was part of the 18th International Conference on Computer Aided Verification.

Model Theory in Algebra, Analysis and Arithmetic

Model Theory in Algebra, Analysis and Arithmetic
Author: Lou van den Dries
Publisher: Springer
Total Pages: 201
Release: 2014-09-20
Genre: Mathematics
ISBN: 3642549365

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.