On hereditarily rigid algebras
type: Item
instance of: scholarly article
title: On hereditarily rigid algebras
zbMATH Open document ID: 0604.08001
DOI: 10.1007/BF01224019
author: Vojtěch Rödl
author: Václav Koubek
published in: Algebra Universalis
publication date: 1986-01-01T00:00:00Z
review text: An algebra A is said to be hereditarily rigid if every subalgebra of A has only one endomorphism. Let t be a similarity type; denote by R(t) the least cardinal number (if it exists) such that no t-algebra of cardinality \(\geq R(t)\) is hereditarily rigid. It is proved that if t is infinitary then R(t) does not exist; if t is unary then R(t) exists, and good bounds for this cardinal are found. If t is finitary and non-unary then R(t), if it exists, is strongly inaccessible. It is consistent with ZFC to assume one of the following possibilities: for every finitary non- unary t, R(t) does not exist; for every finitary t, R(t) exists; there are two finitary non-unary types t,t' such that R(t) does exist and R(t') does not exist.
Mathematics Subject Classification ID: 08A35
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 08A60
Mathematics Subject Classification ID: 08A65
zbMATH DE Number: 3975004
zbMATH Keywords: hereditarily rigid
zbMATH Keywords: subalgebra
zbMATH Keywords: endomorphism
zbMATH Keywords: similarity type
zbMATH Keywords: infinitary
zbMATH Keywords: strongly inaccessible
zbMATH Keywords: consistent with ZFC
zbMATH Keywords: finitary non- unary
reviewed by: Jaroslav Ježek
MaRDI profile type: Publication
cites work: On the structure of set-mappings
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cites work: Über Abbildungen von Mengen
cites work: Q3208855
description: scientific article; zbMATH DE number 3975004