Models for short sequences of measures in the cofinality$\omega$ constructible model
Abstract
We investigate the relation between $C^{*}$, the model of sets constructible using first order logic augmented with the "cofinality$\omega$" quantifier, and "short" sequences of measures  sequences of measures of order $1$, which are shorter than their minimum. We show that certain core models for short sequences of measures are contained in $C^{*}$; we compute $C^{*}$ in a model of the form $L\left[\mathcal{U}\right]$ where $\mathcal{U}$ is a short sequence of measures, and in models of the form $L\left[\mathcal{U}\right]\left[G\right]$ where $G$ is generic for adding Prikry sequences to some of the measurables of $\mathcal{U}$; and prove that if there is an inner model with a short sequence of measures of order type $\chi$, then there is such an inner model in $C^{*}$.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.04523
 Bibcode:
 2021arXiv210904523Y
 Keywords:

 Mathematics  Logic;
 03E45 (Primary) 03E70;
 03E47;
 03E55 (Secondary)