Models for short sequences of measures in the cofinality-ω constructible model
Abstract
We investigate the relation between C ⁎ , the model of sets constructible using first order logic augmented with the “cofinality- ω ” 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 [ U ] where U is a short sequence of measures, and in models of the form L [ U ] [ G ] where G is generic for adding Prikry sequences to some of the measurables of U ; and prove that if there is an inner model with a short sequence of measures of order type χ , then there is such an inner model in C ⁎ .
Fields of Study & Subjects
Computability
Logic
AI Algorithms
Advanced Algebra and Logic
semigroups and automata theory
Publication details
- Journal / source
- Annals of Pure and Applied Logic
- Publisher
- Elsevier BV
- Volume
- 177
- Issue
- 9
- Pages
- 103777–103777
- Publication date
- 22 April 2026
- Language
- EN