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Zermelo writes in [61, p. 262] that he was not able to show that the seven axioms for Set Theory given in that article are consistent. Even though it is essential whether a theory is consistent or not, we know that whenever a theory is strong enough to prove the axioms of PA, then there is no way to prove its consistency within this theory (see Chapter 11).

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Models of Set Theory

  • 章节

  • 发表日期：

    2025年

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  • Lorenz Halbeisen,
  • Regula Krapf

摘要

Zermelo writes in [61, p. 262] that he was not able to show that the seven axioms for Set Theory given in that article are consistent. Even though it is essential whether a theory is consistent or not, we know that whenever a theory is strong enough to prove the axioms of PA, then there is no way to prove its consistency within this theory (see Chapter 11).