Corrigendum to “Structure and electrochemical behavior of lithium vanadate materials for lithium batteries” [Electrochimica Acta 51 (2006) 5973–5981]
- 作者：Atef Y. Shenouda
- 关键词：Easton’ ; s theorem ; Hypermeasurable and strong cardinals ; Lifting
- 刊名：Electrochimica Acta
- 出版年：2008
- 期刊代码：30_00134686
- 类别：ch
- 出版时间：20 August 2008
- 卷：53
- 期：20
- 页码：6055
- 文件大小：140 K
摘要
The continuum function 
2 on regular cardinals is known to have great freedom. Let us say that F is an Easton function iff for regular cardinals and 175003826b83da58faf2531343e" title="Click to view the MathML source" alt="Click to view the MathML source">β, 
and <β→F()≤F(β). The classic example of an Easton function is the continuum function 2 on regular cardinals. If GCH holds then any Easton function is the continuum function on regular cardinals of some cofinality-preserving extension V[G]; we say that F is realised in V[G]. However if we also wish to preserve measurable cardinals, new restrictions must be put on F. We say that κ is F(κ)-hypermeasurable iff there is an elementary embedding j:V→M with critical point κ such that H(F(κ))V
M; j will be called a witnessing embedding. We will show that if GCH holds then for any Easton function F there is a cofinality-preserving generic extension V[G] such that if κ, closed under F, is F(κ)-hypermeasurable in V and there is a witnessing embedding ebaad96f890cb7225d960213b" title="Click to view the MathML source" alt="Click to view the MathML source">j such that j(F)(κ)≥F(κ), then κ will remain measurable in eba3067e9183ad11" title="Click to view the MathML source" alt="Click to view the MathML source">V[G].
2 on regular cardinals is known to have great freedom. Let us say that F is an Easton function iff for regular cardinals and 175003826b83da58faf2531343e" title="Click to view the MathML source" alt="Click to view the MathML source">β, <β→F()≤F(β). The classic example of an Easton function is the continuum function 2 on regular cardinals. If GCH holds then any Easton function is the continuum function on regular cardinals of some cofinality-preserving extension V[G]; we say that F is realised in V[G]. However if we also wish to preserve measurable cardinals, new restrictions must be put on F. We say that κ is F(κ)-hypermeasurable iff there is an elementary embedding j:V→M with critical point κ such that H(F(κ))VM; j will be called a witnessing embedding. We will show that if GCH holds then for any Easton function F there is a cofinality-preserving generic extension V[G] such that if κ, closed under F, is F(κ)-hypermeasurable in V and there is a witnessing embedding ebaad96f890cb7225d960213b" title="Click to view the MathML source" alt="Click to view the MathML source">j such that j(F)(κ)≥F(κ), then κ will remain measurable in eba3067e9183ad11" title="Click to view the MathML source" alt="Click to view the MathML source">V[G].