Definable partitions and reflection properties for regular cardinals
type: Item
instance of: scholarly article
title: Definable partitions and reflection properties for regular cardinals
zbMATH Open document ID: 0585.03024
author: Evangelos Kranakis
published in: Notre Dame Journal of Formal Logic
publication date: 1985-01-01T00:00:00Z
review text: Let \(\kappa\) \(\to^{\Sigma_ n}(\kappa)^ 2_ 2\) mean that every partition of \([\kappa]^ 2\) into two sets defined by a \(\Sigma_ n\)- formula has a homogeneous set of order type \(\kappa\). Let for every n \(\kappa_ n\) be the first \(\kappa\) for which \(\kappa\) \(\to^{\Sigma_ n}(\kappa)^ 2_ 2\). The author relates the above partition properties to certain \(\Pi^ 1_ 1-reflection\) properties. It follows that assuming \(V=L\) the \(\kappa_ n\) lie between the first inaccessible and the first Mahlo cardinal. In particular \(\kappa_ 2\) lies strictly between these cardinals. It is left open whether \(\kappa_ 1\) is the first inaccessible and whether in general \(\kappa_ n<\kappa_{n+1}\).
reviewed by: K. P. Hart
Mathematics Subject Classification ID: 03E45
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E47
Mathematics Subject Classification ID: 03E05
zbMATH DE Number: 3937169
zbMATH Keywords: definable partitions
zbMATH Keywords: homogeneous set
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093870931
OpenAlex ID: W2051889348
DOI: 10.1305/NDJFL/1093870931
description: scientific article; zbMATH DE number 3937169