Beyond First Order Model Theory, Volume II
暫譯: 超越一階模型理論，第二卷
Iovino, Jose
- 出版商: CRC
- 出版日期: 2023-07-03
- 售價: $6,200
- 貴賓價: 9.5 折 $5,890
- 語言: 英文
- 頁數: 300
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 0367208261
- ISBN-13: 9780367208264
-
相關分類:
邏輯設計 Logic-design
海外代購書籍(需單獨結帳)
相關主題
商品描述
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.
商品描述(中文翻譯)
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（Afred Tarski）創造了「模型理論」（Theory of Models）這個術語，並迅速成為數學邏輯中最活躍的核心分支之一。在過去幾十年中，源於模型理論的思想為解決各種古典數學領域的問題提供了強大的工具，包括代數、組合學、幾何、數論以及巴拿赫空間理論和算子理論。
《超越一階模型理論》（Beyond First Order Model Theory）這兩卷書為讀者提供了一個相當全面的視野，涵蓋當代模型理論中一些最活躍的研究領域，超越了古典一階觀點的範疇。每一章旨在作為當前模型理論方向的介紹，以及呈現其他地方無法獲得的研究結果。所有文章的撰寫方式使其可以獨立於彼此進行學習。
這第二卷包含了對實值邏輯及其應用、抽象初等類別及其應用、模型理論與函數空間之間的相互關聯、非結構理論以及二階邏輯的模型理論的介紹。
特色
- 對當前模型理論趨勢的連貫介紹。
- 包含過去一百年中一些最具影響力的邏輯學家的文章。沒有其他出版物能將這些傑出的作者聚集在一起。
- 適合作為高年級本科生、研究生和研究人員的參考資料。
- 書中呈現的材料（例如，抽象初等類別、具有依賴類型的一階邏輯，以及在集合論中無窮邏輯的應用）在當前文獻中不易獲得。
- 書中的各個章節可以獨立學習。
作者簡介
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).
作者簡介(中文翻譯)
Jose Iovino 是德克薩斯州聖安東尼奧大學的數學教授。他的研究領域為模型理論及其應用。他是專著 Applications of Model Theory to Functional Analysis（Dover Publications, 2014）的作者，也是 Analysis and Logic（劍橋大學出版社, 2003）的共同作者，以及 Beyond First Order Model Theory（CRC Press, 2017）第一卷的編輯。
