Corpus ID: 237491995

Iterating the cofinality-$\omega$ constructible model

  title={Iterating the cofinality-\$\omega\$ constructible model},
  author={Ur Ya'ar},
  • 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. 


On sequences generic in the sense of Prikry
I establish here a criterion for a sequence of ordinals to be generic over a transitive model of ZFC with respect to a notation of forcing first considered by Prikry in his Doctoral dissertation [2].Expand
Consistency results about ordinal definability
Transfinite descending sequences of models HODα
Iterated ultrapowers and prikry forcing
Forcing with trees and ordinal definability
Changing cofinality of a measurable cardinal (an alternative proof)
  • Commentationes Mathematicae Universitatis Carolinae
  • 1973
On the sequence of models HODn
  • Consistency results about ordinal definability
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