School of Mathematics and Statistics - Research Publications
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ItemTREEABLE EQUIVALENCE RELATIONS(WORLD SCIENTIFIC PUBL CO PTE LTD, 2012-06-01)There are continuum many ≤B-incomparable equivalence relations induced by a free, Borel action of a countable non-abelian free group — and hence, there are 2α0 many treeable countable Borel equivalence relations which are incomparable in the ordering of Borel reducibility.
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ItemA converse to Dye's theorem(AMER MATHEMATICAL SOC, 2005-01-01)
Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of F 2 \mathbb {F}_2 on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not universal for treeable in the ≤ B \leq _B ordering.
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ItemEFFECTIVE CARDINALS OF BOLDFACE POINTCLASSES(World Scientific Pub Co Pte Lt, 2007-06)Assuming AD + DC(ℝ), we characterize the self-dual boldface pointclasses which are strictly larger (in terms of cardinality) than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank [Formula: see text], and those of Wadge rank [Formula: see text] when ξ is limit.
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ItemThe classification problem for p-local torsion-free abelian groups of rank two(WORLD SCIENTIFIC PUBL CO PTE LTD, 2006-12-01)We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.
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ItemNon-treeability for product group actions(HEBREW UNIV MAGNES PRESS, 2008-01-01)
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