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Titlebook: Mathematical Logic; On Numbers, Sets, St Roman Kossak Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), under ex

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发表于 2025-3-21 18:20:05 | 显示全部楼层 |阅读模式
书目名称Mathematical Logic
副标题On Numbers, Sets, St
编辑Roman Kossak
视频video
概述New edition includes countable categoricity, analyzed using examples from the first two parts of the book.Presents an introduction to formal mathematical logic and set theory.Presents simple yet nontr
丛书名称Springer Graduate Texts in Philosophy
图书封面Titlebook: Mathematical Logic; On Numbers, Sets, St Roman Kossak Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), under ex
描述.This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions...Part I, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are usedto study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced a
出版日期Textbook 2024Latest edition
关键词first-order logic introduction; Abstract symmetries; Number system development; Model theory; Formal ari
版次2
doihttps://doi.org/10.1007/978-3-031-56215-0
isbn_ebook978-3-031-56215-0Series ISSN 2627-6046 Series E-ISSN 2627-6054
issn_series 2627-6046
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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发表于 2025-3-21 23:52:37 | 显示全部楼层
Logical Seeinger, logic will help us to see structures; now, simple structures will help us to see logic. A concept of symmetry of a graph is introduced in Definition 2.1 followed by Theorem 2.1, which is crucial for many further developments. Both, the definition and the theorem, will be generalized later to arbitrary mathematical structures.
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Points, Lines, and the Structure of ow seemingly innocuous assumptions about actually infinite sets lead to consequences that are not easy to accept. Then, we will go back to our discussion of a formal approach that will help to make some sense out of it.
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Geometry of Definable Setsorrespond in a natural way to Boolean connectives and quantifiers, and how the name “geometry” is justified when it is applied to sets definable in the field of real numbers. The last two sections are devoted to a discussion of the negative solution to Hilbert’s 10th problem.
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Seeing the Number Structureserms of first-order logic. The reconstruction is technical and rather tedious, but it serves as a good example of how some mathematical structures can bee seen inside other structures with the eyes of logic. This chapter can be skipped on the first reading, but it should not be forgotten.
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Roman KossakNew edition includes countable categoricity, analyzed using examples from the first two parts of the book.Presents an introduction to formal mathematical logic and set theory.Presents simple yet nontr
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