On a Spector Ultrapower for the Solovay Model

DOI10.1002/MALQ.19970430311zbMATH Open0877.03024arXivmath/9502205OpenAlexW2125337180MaRDI QIDQ4351928

Vladimir Kanovei, Michiel van Lambalgen

Publication date: 8 December 1997

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Abstract: We prove that a Spector--like ultrapower extension $gN$ of a countable Solovay model $gM$ (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension $gM[al]$ where $al$ is a random real over $gM.$ The proof involves an almost everywhere uniformization theorem in the Solovay model.

Full work available at URL: https://arxiv.org/abs/math/9502205

zbMATH Keywords

axiom of choicerandom realaxiom of dependent choicecountable Solovay modelultrapowers of models of set theory

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Axiom of choice and related propositions (03E25) Other aspects of forcing and Boolean-valued models (03E40) Determinacy principles (03E60)

This page was built for publication: On a Spector Ultrapower for the Solovay Model

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4351928)