A note on counterexamples to the Vaught conjecture
type: Item
instance of: scholarly article
title: A note on counterexamples to the Vaught conjecture
zbMATH Open document ID: 1128.03024
author: Greg Hjorth
published in: Notre Dame Journal of Formal Logic
publication date: 2007-08-10T00:00:00Z
review text: In this short note the following consequence of a previous theorem by the author [J. Math. Log. 2, 113--144 (2002; Zbl 1010.03036)] is proved: if Vaught's conjecture for \(\mathcal{L}_{\omega_1 \omega}\) is false then there is a counterexample with no models of cardinality larger than \(\aleph_1\). The proof uses tools from descriptive set theory and in particular from the study of Polish groups actions.
reviewed by: Alberto Marcone
Mathematics Subject Classification ID: 03C75
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 03C55
zbMATH DE Number: 5178765
zbMATH Keywords: Vaught's conjecture
zbMATH Keywords: infinitary logic
zbMATH Keywords: Polish groups actions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1172787544
OpenAlex ID: W2086807244
Wikidata QID: Q122960655
DOI: 10.1305/NDJFL/1172787544
description: scientific article; zbMATH DE number 5178765