Finite powers and products of Menger sets
نویسندگان
چکیده
We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two sets are in all finite powers, with non-Menger product. By forcing-theoretic argument, we show the same holds Blass–Shelah
منابع مشابه
Finite Powers of Strong Measure Zero Sets
In a previous paper – [17] – we characterized strong measure zero sets of reals in terms of a Ramseyan partition relation on certain subspaces of the Alexandroff duplicate of the unit interval. This framework gave only indirect access to the relevant sets of real numbers. We now work more directly with the sets in question, and since it costs little in additional technicalities, we consider the...
متن کاملOn sets of integers whose shifted products are powers
Let N be a positive integer and let A be a subset of {1, . . . , N} with the property that aa′ + 1 is a pure power whenever a and a′ are distinct elements of A. We prove that |A|, the cardinality of A, is not large. In particular, we show that |A| ≪ (logN)2/3(log logN)1/3.
متن کاملCountable Products of Spaces of Finite Sets
σn(Γ) = {x ∈ {0, 1} Γ : |supp(x)| ≤ n}. Here supp(x) = {γ ∈ Γ : xγ 6= 0}. This is a closed, hence compact subset of {0, 1}, which is identified with the family of all subsets of Γ of cardinality at most n. In this work we will study the spaces which are countable products of spaces σn(Γ), mainly their topological classification as well as the classification of their Banach spaces of continuous ...
متن کاملQueue Layouts of Graph Products and Powers
A k-queue layout of a graph G consists of a linear order σ of V (G), and a partition of E(G) into k sets, each of which contains no two edges that are nested in σ. This paper studies queue layouts of graph products and powers.
متن کاملInfinite Power and Finite Powers∗
The etymological meaning of ‘omnipotent’ is ‘all-powerful.’ Being all-powerful is usually understood as having all of the powers. The problem of analyzing omnipotence is then seen as the problem of determining over what class the quantifier ‘all’ in this assertion ranges. An omnipotent being would be one that has all of the powers; all of what powers? Attempts to answer this question have run i...
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: Fundamenta Mathematicae
سال: 2021
ISSN: ['0016-2736', '1730-6329']
DOI: https://doi.org/10.4064/fm896-4-2020