Corpus ID: 237491995

Iterating the cofinality-$\omega$ constructible model

@inproceedings{Yaar2021IteratingTC,
  title={Iterating the cofinality-\$\omega\$ constructible model},
  author={Ur Ya'ar},
  year={2021}
}
  • Ur Ya'ar
  • Published 13 September 2021
  • Mathematics
We investigate iterating the construction of C∗, theL-like inner model constructed using first order logic augmented with the “cofinalityω” quantifier. We first show that (C∗) ∗ = C 6= L is equiconsistent with ZFC, as well as having finite strictly decreasing sequences of iterated Cs. We then show that in models of the form L we get infinite decreasing sequences of length ω, and that an inner model with a measurable cardinal is required for that. 

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