Two undecidable questions about group actions

John P. Burgess

doi:10.1007/s13171-010-0015-4

Two undecidable questions about group actions

John P. Burgess

Philosophy

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

Abstract

It is shown that for invariance under the action of special groups the statements “Every invariant PCA is decomposable into ℵ₁ invariant Borel sets” and “Every pair of invariant PCA is reducible by a pair of invariant PCA sets” are independent of the axioms of set theory.

Original language	English (US)
Pages (from-to)	64-69
Number of pages	6
Journal	Sankhya A
Volume	72
Issue number	1
DOIs	https://doi.org/10.1007/s13171-010-0015-4
State	Published - Feb 1 2010

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1007/s13171-010-0015-4

Cite this

@article{234bd574f78b4d70b5afc125f10824fa,

title = "Two undecidable questions about group actions",

abstract = "It is shown that for invariance under the action of special groups the statements “Every invariant PCA is decomposable into ℵ1 invariant Borel sets” and “Every pair of invariant PCA is reducible by a pair of invariant PCA sets” are independent of the axioms of set theory.",

author = "Burgess, {John P.}",

note = "Publisher Copyright: {\textcopyright} 2010, Indian Statistical Institute.",

year = "2010",

month = feb,

day = "1",

doi = "10.1007/s13171-010-0015-4",

language = "English (US)",

volume = "72",

pages = "64--69",

journal = "Sankhya A",

issn = "0976-836X",

publisher = "Springer India",

number = "1",

}

TY - JOUR

T1 - Two undecidable questions about group actions

AU - Burgess, John P.

PY - 2010/2/1

Y1 - 2010/2/1

N2 - It is shown that for invariance under the action of special groups the statements “Every invariant PCA is decomposable into ℵ1 invariant Borel sets” and “Every pair of invariant PCA is reducible by a pair of invariant PCA sets” are independent of the axioms of set theory.

AB - It is shown that for invariance under the action of special groups the statements “Every invariant PCA is decomposable into ℵ1 invariant Borel sets” and “Every pair of invariant PCA is reducible by a pair of invariant PCA sets” are independent of the axioms of set theory.

UR - http://www.scopus.com/inward/record.url?scp=85034567079&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034567079&partnerID=8YFLogxK

U2 - 10.1007/s13171-010-0015-4

DO - 10.1007/s13171-010-0015-4

M3 - Article

AN - SCOPUS:85034567079

SN - 0976-836X

VL - 72

SP - 64

EP - 69

JO - Sankhya A

JF - Sankhya A

IS - 1

ER -

Two undecidable questions about group actions

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this