A countable structure does not have a free uncountable automorphism group

Saharon Shelah

doi:10.1112/S0024609302001534

A countable structure does not have a free uncountable automorphism group

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

It is proved that the automorphism group of a countable structure cannot be a free uncountable group. The idea is that instead of proving that every countable set of equations of a certain form has a solution, it is proved that this holds for a co-meagre family of appropriate countable sets of equations.

Original language	English
Pages (from-to)	1-7
Number of pages	7
Journal	Bulletin of the London Mathematical Society
Volume	35
Issue number	1
DOIs	https://doi.org/10.1112/S0024609302001534
State	Published - Jan 2003

Access to Document

10.1112/S0024609302001534

Cite this

@article{ff7f1fbac8e94e079ef51beb05610120,

title = "A countable structure does not have a free uncountable automorphism group",

abstract = "It is proved that the automorphism group of a countable structure cannot be a free uncountable group. The idea is that instead of proving that every countable set of equations of a certain form has a solution, it is proved that this holds for a co-meagre family of appropriate countable sets of equations.",

author = "Saharon Shelah",

year = "2003",

month = jan,

doi = "10.1112/S0024609302001534",

language = "אנגלית",

volume = "35",

pages = "1--7",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "1",

}

TY - JOUR

T1 - A countable structure does not have a free uncountable automorphism group

AU - Shelah, Saharon

PY - 2003/1

Y1 - 2003/1

N2 - It is proved that the automorphism group of a countable structure cannot be a free uncountable group. The idea is that instead of proving that every countable set of equations of a certain form has a solution, it is proved that this holds for a co-meagre family of appropriate countable sets of equations.

AB - It is proved that the automorphism group of a countable structure cannot be a free uncountable group. The idea is that instead of proving that every countable set of equations of a certain form has a solution, it is proved that this holds for a co-meagre family of appropriate countable sets of equations.

UR - http://www.scopus.com/inward/record.url?scp=0037256210&partnerID=8YFLogxK

U2 - 10.1112/S0024609302001534

DO - 10.1112/S0024609302001534

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0037256210

SN - 0024-6093

VL - 35

SP - 1

EP - 7

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 1

ER -

A countable structure does not have a free uncountable automorphism group

Abstract

Access to Document

Other files and links

Fingerprint

Cite this