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Primitive recursive analogues of regular cardinals based on ordinal representation systems for KPi and KPM

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Abstract

In this paper, we develop primitive recursive analogues of regular cardinals by using ordinal representation systems for KPi and KPM. We also define primitive recursive analogues of inaccessible and hyperinaccessible cardinals. Moreover, we characterize the primitive recursive analogue of the least (uncountable) regular cardinal.

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Correspondence to Osamu Takaki.

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Takaki, O. Primitive recursive analogues of regular cardinals based on ordinal representation systems for KPi and KPM. Arch. Math. Logic 44, 689–709 (2005). https://doi.org/10.1007/s00153-005-0308-9

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Key words or phrases

  • Proof-theoretic ordinal
  • Ordinal representation system
  • Inaccessible cardinal