Beyond First Order Model Theory, Volume II

Model theory is the meta-mathematical study of the concept of mathematical truth. After Afred Tarski coined the term Theory of Models in the early 1950's, it rapidly became one of the central most active branches of mathematical logic. In the last few decades, ideas that originated within model theory have provided powerful tools to solve problems in a variety of areas of classical mathematics, including algebra, combinatorics, geometry, number theory, and Banach space theory and operator theory.

The two volumes of Beyond First Order Model Theory present the reader with a fairly comprehensive vista, rich in width and depth, of some of the most active areas of contemporary research in model theory beyond the realm of the classical first-order viewpoint. Each chapter is intended to serve both as an introduction to a current direction in model theory and as a presentation of results that are not available elsewhere. All the articles are written so that they can be studied independently of one another.

This second volume contains introductions to real-valued logic and applications, abstract elementary classes and applications, interconnections between model theory and function spaces, nonstucture theory, and model theory of second-order logic.

Features

• A coherent introduction to current trends in model theory.
• Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together.
• Suitable as a reference for advanced undergraduate, postgraduates, and researchers.
• Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature.
• The various chapters in the book can be studied independently.

模型理論是對數學真理概念的元數學研究。在1950年代初，阿爾弗雷德·塔斯基（Alfred Tarski）創造了「模型理論」這個術語後，它迅速成為數學邏輯中最活躍的分支之一。在過去幾十年中，模型理論中產生的思想為解決古典數學的各個領域（包括代數、組合學、幾何學、數論、Banach空間理論和算子理論）的問題提供了強大的工具。

《超越一階模型理論》的兩卷本為讀者呈現了一個相當全面的視野，深度廣度兼具，介紹了當代模型理論研究中一些最活躍的領域，超越了古典一階觀點的範疇。每一章都旨在作為模型理論中當前方向的介紹，同時呈現一些其他地方無法找到的結果。所有文章都可以獨立學習。

這本第二卷包含了對實值邏輯及其應用、抽象基本類及其應用、模型理論與函數空間之間的相互聯繫、非結構理論以及二階邏輯的模型理論的介紹。

特點：
- 對模型理論當前趨勢的一個有條理的介紹。
- 包含一些最有影響力的邏輯學家撰寫的文章。沒有其他出版物將這些傑出的作者聚集在一起。
- 適合高年級本科生、研究生和研究人員參考。
- 本書中介紹的材料（例如抽象基本類、具有依賴排序的一階邏輯以及在集合論中應用無窮邏輯）在當前文獻中不容易找到。
- 本書中的各個章節可以獨立學習。

Jose Iovino is a professor of Mathematics at The University of Texas at San Antonio. His research is in model theory and its applications. He is the author of the monograph Applications of Model Theory to Functional Analysis (Dover Publications, 2014), a co-author of Analysis and Logic (Cambridge University Press, 2003), and the editor of the first volume of Beyond First Order Model Theory (CRC Press, 2017).

Jose Iovino是德州大學聖安東尼奧分校的數學教授。他的研究領域是模型理論及其應用。他是著有專著《模型理論在泛函分析中的應用》（Dover Publications，2014）的作者，也是《分析與邏輯》（劍橋大學出版社，2003）的合著者，以及《超越一階模型理論》（CRC Press，2017）第一卷的編輯。