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In this chapter, we introduce the main objects of study throughout this book, namely metric structures, as well as the associated continuous logic suitable for analyzing them from a logical perspective. The reader interested in further references for the material presented in this chapter may consult [1, 2]. We intend to use this logic as a foundation for studying the computability of these structures. In Chaps.  7 and 8 , we will see the interplay between the model theory and computability theory of metric structures.

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An Introduction to Metric Structures and Their Model Theory

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  • 发表日期：

    2026年

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  • Johanna N. Y. Franklin,
  • Isaac Goldbring,
  • Timothy H. McNicholl

摘要

In this chapter, we introduce the main objects of study throughout this book, namely metric structures, as well as the associated continuous logic suitable for analyzing them from a logical perspective. The reader interested in further references for the material presented in this chapter may consult [1, 2]. We intend to use this logic as a foundation for studying the computability of these structures. In Chaps.  7 and 8 , we will see the interplay between the model theory and computability theory of metric structures.