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Chapter 2 introduced propositional and predicate logic and showed how to model the reasoning principles of ordinary mathematics within a for-mal system. This chapter will extend predicate logic to so-called the-ories by adding new axioms. In a nutshell, a mathematical theory is a formal system whose axioms are divided into two groups: non-logical and logical axioms.

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Foundations of Mathematics

  • 章节

  • 发表日期：

    2025年

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  • Dirk W. Hoffmann

摘要

Chapter 2 introduced propositional and predicate logic and showed how to model the reasoning principles of ordinary mathematics within a for-mal system. This chapter will extend predicate logic to so-called the-ories by adding new axioms. In a nutshell, a mathematical theory is a formal system whose axioms are divided into two groups: non-logical and logical axioms.