650 research outputs found
On Martin's Pointed Tree Theorem
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)
Non-unique ergodicity, observers' topology and the dual algebraic lamination for -trees
We continue in this article the study of laminations dual to very small
actions of a free group F on R-trees. We prove that this lamination determines
completely the combinatorial structure of the R-tree (the so-called observers'
topology). On the contrary the metric is not determined by the lamination, and
an R-tree may be equipped with different metrics which have the same observers'
topology.Comment: to appear in the Illinois Journal of Mat
Proper forcings and absoluteness in
We show that in the presence of large cardinals proper forcings do not change the theory of with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model
A study of computational aspects of network models for planning and control
Beginning with the PERT-CPM methodology and progressing through the more general network models, this study critically reviews the computational assumptions, results and possible errors, both by character and magnitude
Some interesting problems
A ≤W B. (This refers to Wadge reducible.) Answer: The first question was answered by Hjorth [83] who showed that it is independent. 1.2 A subset A ⊂ ω ω is compactly-Γ iff for every compact K ⊂ ω ω we have that A ∩ K is in Γ. Is it consistent relative to ZFC that compactly-Σ 1 1 implies Σ 1 1? (see Miller-Kunen [111], Becker [11]) 1.3 (Miller [111]) Does ∆ 1 1 = compactly- ∆ 1 1 imply Σ 1 1 = compactly-Σ 1 1? 1.4 (Prikry see [62]) Can L ∩ ω ω be a nontrivial Σ 1 1 set? Can there be a nontrivial perfect set of constructible reals? Answer: No, for first question Velickovic-Woodin [192]. question Groszek-Slaman [71]. See also Gitik [67]
A strong antidiamond principle compatible with CH
A strong antidiamond principle (*c) is shown to be consistent with CH. This
principle can be stated as a "P-ideal dichotomy": every P-ideal on omega-1
(i.e. an ideal that is sigma-directed under inclusion modulo finite) either has
a closed unbounded subset of omega-1 locally inside of it, or else has a
stationary subset of omega-1 orthogonal to it. We rely on Shelah's theory of
parameterized properness for NNR iterations, and make a contribution to the
theory with a method of constructing the properness parameter simultaneously
with the iteration. Our handling of the application of the NNR iteration theory
involves definability of forcing notions in third order arithmetic, analogous
to Souslin forcing in second order arithmetic.Comment: 54 pages (Elsevier article style). To appear in Annals of Pure and
Applied Logic. Homepage:
http://homepage.univie.ac.at/James.Hirschorn/research/strong.antidiamond/strong.antidiamond.htm
Degrees that are low for isomorphism
We say that a degree is low for isomorphism if, whenever it can compute an isomorphism between a pair of computable structures, there is already a computable isomorphism between them. We show that while there is no clear-cut relationship between this property and other properties related to computational weakness, the low-forisomorphism degrees contain all Cohen 2-generics and are disjoint from the Martin-Löf randoms. We also consider lowness for isomorphism with respect to the class of linear orders.
- …