Definable sets of generators in maximal cofinitary groups

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• 作者：Su Gao ; Yi Zhang
• 关键词：Maximal cofinitary groups ; Definability ; Axiom of constructability
• 刊名：Advances in Mathematics
• 出版年：2008
• 出版时间：30 January 2008
• 年：2008
• 卷：217
• 期：2
• 页码：814-832
• 全文大小：185 K

文摘

A group W9F-4PXP0WK-2&_mathId=mml1&_user=10&_cdi=6681&_rdoc=13&_acct=C000050221&_version=1&_userid=10&md5=30b8fae0d912e82fb847bcca58939697"">www.sciencedirect.com/cache/MiamiImageURL/B6W9F-4PXP0WK-2-2/0?wchp=dGLbVtz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=15 width=84> is cofinitary if g has finitely many fixed points for every w the MathML source"">gwww.sciencedirect.com/scidirimg/entities/2208.gif"" alt=""set membership, variant"" border=0>G except the identity element. In this paper, we discuss the definability of maximal cofinitary groups and some related structures. More precisely, we show the following two results:

(1) Assuming w the MathML source"">V=L, there is a a38572"">www.sciencedirect.com/cache/MiamiImageURL/B6W9F-4PXP0WK-2-5/0?wchp=dGLbVtz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=20 width=22> set of permutations on www.sciencedirect.com/cache/MiamiImageURL/B6W9F-4PXP0WK-2-6/0?wchp=dGLbVtz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=13 width=13> which generates a maximal cofinitary group.

(2) Assuming w the MathML source"">V=L, there is a www.sciencedirect.com/cache/MiamiImageURL/B6W9F-4PXP0WK-2-8/0?wchp=dGLbVtz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=20 width=22> mad permutation family in www.sciencedirect.com/cache/MiamiImageURL/B6W9F-4PXP0WK-2-9/0?wchp=dGLbVtz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=15 width=53>.