9 citations · 9 across the 6 of their papers we have counts for
8 papers
Order-preserving maps of the Turing degrees: regularity and consistency strength
Liang Yu
We formulate a proof of Part~I of Martin's conjecture for order-preserving maps directly on the quotient of the reals by Turing equivalence. The assumptions are countable choice fo…
Small additive groups with
Liang Yu
We prove that, for every irrational , any additive subgroup of has an $\Q$-vector space extension of the same Hausdorff dimension satisfying . Iteratio…
Some more results on relativized Chaitin's
Liang Yu
We prove that, assuming , and restricted to any pointed set, Chaitin's is not injective for any universal prefix-f…
TD implies CCR
Yinhe Peng, Liang Yu
Assuming , we prove that Turing determinacy () implies countable choice axiom for sets of reals ().
Luzin's (N) and randomness reflection
Arno Pauly, Linda Westrick, Liang Yu
We show that a computable function has Luzin's property (N) if and only if it reflects -randomnes, if and only if it reflects $Δ^1_1(\mathc…
A model with everything except for a well-ordering of the reals
Jörg Brendle, Fabiana Castiblanco, Ralf Schindler +2
We construct a model of containing a Luzin set, a Sierpiński set, as well as a Burstin basis but in which there is no a well ordering of the continuum.
Higher Kurtz randomness
Bjørn Kjos-Hanssen, André Nies, Frank Stephan +1
A real is -Kurtz random (-Kurtz random) if it is in no closed null set ( set). We show that there is a cone of -Kurtz random hyperdegrees. W…
On Martin's Pointed Tree Theorem
Rupert Hölzl, Frank Stephan, Liang Yu
We investigate the reverse mathematics strength of Martin's pointed tree theorem (MPT) and one of its variants, weak Martin's pointed tree theorem (wMPT).