COMPUTABLE ANALYSIS AND BLASCHKE PRODUCTS (2008)
Alec Matheson, H. Mcnicholl, Communicated Julia Knight
Dedicated to the memory of Alec Matheson. Abstract. We show that if a Blaschke product defines a computable function, then it has a computable sequence of zeros in which the number of times each zero...
When van Lambalgen’s Theorem fails (2008)
Liang Yu, Communicated Julia Knight
Abstract. We prove that van Lambalgen’s Theorem fails for both Schnorr randomness and computable randomness. To characterize randomness, various definitions of randomness for individual elements of...
LARGE CARDINALS WITH FEW MEASURES (2008)
Arthur W. Apter, James Cummings, David Hamkins, Communicated Julia Knight
Abstract. We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly κ + many normal measures on the least measurable cardinal κ. This answers a...
COFINALITY CHANGES REQUIRED FOR A LARGE SET OF UNAPPROACHABLE ORDINALS BELOW ℵω+1 (2008)
M. C. Stanley, Communicated Julia Knight
Abstract. In V, assume that ℵω is a strong limit cardinal and 2 ℵω = ℵω+1. Let A be the set of approachable ordinals less than ℵω+1. Anopenquestion of M. Foreman is whether A can be...
ON THE COMPUTABILITY-THEORETIC COMPLEXITY OF TRIVIAL, STRONGLY MINIMAL MODELS (2008)
Bakhadyr M. Khoussainov, Michael C. Laskowski, Steffen Lempp, Reed Solomon, Communicated Julia Knight
Abstract. We show the existence of a trivial, strongly minimal (and thus uncountably categorical) theory for which the prime model is computable and each of the other countable models computes 0 ′...
COUNTABLE COMPACT HAUSDORFF SPACES NEED NOT BE METRIZABLE IN ZF (2008)
Kyriakos Keremedis, Eleftherios Tachtsis, Communicated Julia Knight
Abstract. We show that the existence of a countable, first countable, zerodimensional, compact Hausdorff space which is not second countable, hence not metrizable, is consistent with ZF. 1. Notation...
MODEL THEORY OF PARTIAL DIFFERENTIAL FIELDS: FROM COMMUTING TO NONCOMMUTING DERIVATIONS (2008)
Michael F. Singer, Communicated Julia Knight
Abstract. McGrail (2000) has shown the existence of a model completion for the universal theory of fields on which a finite number of commuting derivations act and, independently, Yaffe (2001) has...
More on partitioning triples of countable ordinals (2008)
Albin L. Jones, Communicated Julia Knight
Abstract. Consider an arbitrary partition of the triples of all countable ordinals into two classes. We show that either for each finite ordinal m the first class of the partition contains all...
Unprovability of sharp versions of Friedman’s sine-principle (2007)
Andrey Bovykin, Communicated Julia Knight
Abstract. For every n ≥ 1 and every function F of one argument, we introduce the statement SPn F:“forall m, thereisNsuch that for any set A = {a1,a2,...,aN} of rational numbers, there is H ⊆ A...
PARTITIONING TRIPLES AND PARTIALLY ORDERED SETS (2007)
Albin L. Jones, Communicated Julia Knight
Abstract. We prove that if P is a partial order and P → (ω) 1 ω,then (a) P → (ω + ω +1,4) 3,and (b) P → (ω + m, n) 3 for each m, n < ω. Together these results represent the best...
Low for random reals and positive-measure domination (2005)
Bjørn Kjos-hanssen, Communicated Julia Knight
Abstract. The low for random reals are characterized topologically, as well as in terms of domination of Turing functionals on a set of positive measure. 1.