There may be no minimal non-$\sigma$-scattered linear orders
نویسندگان
چکیده
منابع مشابه
There may be no nowhere dense ultrafilter
We show the consistency of ZFC + ”there is no NWD-ultrafilter on ω”, which means: for every non-principal ultrafilter D on the set of natural numbers, there is a function f from the set of natural numbers to the reals, such that for every nowhere dense set A of reals, {n : f(n) ∈ A} / ∈ D. This answers a question of van Douwen, which was put in more general context by Baumgartner. ∗ The researc...
متن کاملThere May Be No Hausdorff Ultrafilters
An ultrafilter U is Hausdorff if for any two functions f, g ∈ ω ω , f (U) = g(U) iff f ↾X = g↾X for some X ∈ U. We will show that it is consistent that there are no Hausdorff ultrafilters.
متن کاملTree-automatic scattered linear orders
We study tree-automatic linear orders on regular tree languages. We first show that there is no tree-automatic scattered linear order, and in particular no well-order, on the set of all finite labeled trees. This also follows from results of Gurevich-Shelah [8] and Carayol-Löding [4]. We then show that a regular tree language admits a tree-automatic scattered linear order if and only if all tre...
متن کاملIsomorphisms of scattered automatic linear orders
We prove that the isomorphism of scattered tree automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders are undecidable. For the existence of automatic automorphisms of word automatic linear orders, we determine the exact level of undecidability in the arithmetical hierarchy.
متن کاملN-Person Cake-Cutting: There May Be No Perfect Division
A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2018
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2018.v25.n6.a13