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Halfway new cardinal characteristics
Annals of Pure and Applied Logic, 2023 Based on the well-known cardinal characteristics $\mathfrak{s}$, $\mathfrak{r}$ and $\mathfrak{i}$, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e. g. the consistency of $\mathfrak{s} < \
Jörg Brendle +2 more
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Higher dimensional cardinal characteristics for sets of functions [PDF]
Annals of Pure and Applied Logic, 2022 Much recent work in cardinal characteristics has focused on generalizing results about $ω$ to uncountable cardinals by studying analogues of classical cardinal characteristics on the generalized Baire and Cantor spaces $κ^κ$ and $2^κ$. In this note I look at generalizations to other function spaces, focusing particularly on the space of functions $f:ω ...
Corey Bacal Switzer
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A Galvin–Hajnal theorem for generalized cardinal characteristics
European Journal of Mathematics, 2023 AbstractWe prove that a variety of generalized cardinal characteristics, including meeting numbers, the reaping number, and the dominating number, satisfy an analogue of the Galvin–Hajnal theorem, and hence also of Silver’s theorem, at singular cardinals of uncountable cofinality.
Chris Lambie-Hanson
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Cardinal characteristics of the continuum and partitions [PDF]
Israel Journal of Mathematics, 2019 We prove combinatorial theorems concerning the stick principle and cardinal characteristics.
Shimon Garti, Thilo Weinert
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Some cardinal characteristics of ordered sets [PDF]
Czechoslovak Mathematical Journal, 1998 Let \(G\) be an ordered set. By a 2-realizer of \(G\) we mean a system \((f_t;t\in T)\) of order-preserving mappings of \(G\) into the 2-element chain such that for any \(x,y\in G\), \(x\leq y\) iff \(f_t(x)\leq f_t(y)\) for all \(t\in T\). The minimal cardinality of a 2-realizer of \(G\) is called the 2-pdim of \(G\).
Vítězslav Novak, Novak Vítězslav
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An Analogy between Cardinal Characteristics and Highness Properties of Oracles [PDF]
Proceedings of the 13th Asian Logic Conference, 2015 We present an analogy between cardinal characteristics from set theory and highness properties from computability theory, which specify a sense in which a Turing oracle is computationally strong. While this analogy was first studied explicitly by Rupprecht in his PhD thesis, many prior results can be viewed from this perspective.
Jörg Brendle +2 more
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Cardinal characteristics, projective wellorders and large continuum
Annals of Pure and Applied Logic, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vera Fischer, Lyubomyr Zdomskyy
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ON CONFIGURATIONS CONCERNING CARDINAL CHARACTERISTICS AT REGULAR CARDINALS [PDF]
The Journal of Symbolic Logic, 2020 AbstractWe study the consistency and consistency strength of various configurations concerning the cardinal characteristics $\mathfrak {s}_\theta , \mathfrak {p}_\theta , \mathfrak {t}_\theta , \mathfrak {g}_\theta , \mathfrak {r}_\theta $ at uncountable regular cardinals $\theta $ .
Omer Ben-Neria, Shimon Garti
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Bounds on the extent of a topological space
Математичні Студії, 2022 The extent $e(X)$ of a topological space $X$ is the supremum of sizes of closed discrete subspaces of $X$. Assuming that $X$ belongs to some class of topological spaces, we bound $e(X)$ by other cardinal characteristics of $X$, for instance Lindel\"of ...
A. Ravsky, T. Banakh
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MUCHNIK DEGREES AND CARDINAL CHARACTERISTICS [PDF]
The Journal of Symbolic Logic, 2020 AbstractA mass problem is a set of functions$\omega \to \omega $. For mass problems${\mathcal {C}}, {\mathcal {D}}$, one says that${\mathcal {C}}$is Muchnik reducible to${\mathcal {D}}$if each function in${\mathcal {C}}$is computed by a function in${\mathcal {D}}$. In this paper we study some highness properties of Turing oracles, which we view as mass
Benoit Monin, André Nies
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