 School of Mathematics and Statistics  Research Publications
School of Mathematics and Statistics  Research Publications
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ItemTREEABLE EQUIVALENCE RELATIONSHjorth, G (WORLD SCIENTIFIC PUBL CO PTE LTD, 201206)There are continuum many ≤Bincomparable equivalence relations induced by a free, Borel action of a countable nonabelian free group — and hence, there are 2α0 many treeable countable Borel equivalence relations which are incomparable in the ordering of Borel reducibility.

ItemA converse to Dye's theoremHjorth, G (AMER MATHEMATICAL SOC, 2005)
Every nonamenable 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 nonhyperfinite Borel equivalence relation which is not universal for treeable in the ≤ B \leq _B ordering.

ItemEFFECTIVE CARDINALS OF BOLDFACE POINTCLASSESANDRETTA, A ; HJORTH, G ; NEEMAN, I (World Scientific Pub Co Pte Lt, 200706)Assuming AD + DC(ℝ), we characterize the selfdual 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.

ItemThe classification problem for plocal torsionfree abelian groups of rank twoHjorth, G ; Thomas, S (WORLD SCIENTIFIC PUBL CO PTE LTD, 200612)We prove that if p ≠ q are distinct primes, then the classification problems for plocal and qlocal torsionfree abelian groups of rank two are incomparable with respect to Borel reducibility.

ItemNontreeability for product group actionsHjorth, G (HEBREW UNIV MAGNES PRESS, 200801)

ItemAn oscillation theorem for groups of isometriesHJORTH, G. ( 2008)

ItemRigidity theorems for actions of product groups and countable Borel equivalence relationsHJORTH, G ; Kechris, AS ( 2005)