On the Ramseyan properties of some special subsets of 2<sup><i>ω</i></sup>and their algebraic sums

Nowik, Andrzej; Weiss, Tomasz

doi:10.2178/jsl/1190150097

Cited by 7 publications

(23 citation statements)

References 9 publications

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“…We will show that The rest of the proof is analogous to the argument from [10], but we present it here for completeness. Assuming CH, let {M α : α ∈ ω 1 } be an enumeration of all meager F σ sets and let {T α : α ∈ ω 1 } be an enumeration of all Laver trees.…”

Section: We Define T ⊆ T By Induction On the Length Of Its Elements mentioning

confidence: 83%

“…By extending t we may always assume that |t| = f (k), where k is minimal such that I Proof. We use similar arguments to those from the proof of Theorem 4.3 in [10]. We need the following lemma.…”

Section: Proposition 34 Every Meager-additive Set X ⊆mentioning

confidence: 99%

“…By a modification of the proof of Theorem 2.2 from [10] one can show that if X is a T -set and Y is strongly meager (see [10] for definitions), then X + Y has the (l 0 )− and the (m 0 )-properties. This obviously gives a different argument for the fact proved in Theorem 3.8.…”

Section: And Consequently ψ [T ] Is a Laver Tree Disjoint With Xmentioning

confidence: 99%

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Special subsets of the reals and tree forcing notions

Kysiak

Weiss

2007

Proc. Amer. Math. Soc.

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Section: We Define T ⊆ T By Induction On the Length Of Its Elements mentioning

confidence: 83%

Section: Proposition 34 Every Meager-additive Set X ⊆mentioning

confidence: 99%

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Special subsets of the reals and tree forcing notions

Kysiak

Weiss

2007

Proc. Amer. Math. Soc.

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“…In this section, we generalize some results presented in [37]. For

α < κ

s \in 2^{α}

and

S \in {[κ ∖ α]}^{κ}

, let

false[s, S false] = {x \in 2^{κ} : s^{- 1} false[{1} false] \subseteq x^{- 1} false[{1} false] \subseteq s^{- 1} false[{1} false] \cup S \land | x^{- 1} false[{1} false] \cap S | = κ}

.…”

Section: Generalization Of Other Notions Of Smallness In 2κ and κκmentioning

confidence: 89%

Special subsets of the generalized Cantor space and generalized Baire space

Korch

Weiss

2020

Mathematical Logic Qtrly

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In this paper, we are interested in parallels to the classical notions of special subsets in R defined in the generalized Cantor and Baire spaces (2 κ and κ κ). We consider generalizations of the well-known classes of special subsets, like Lusin sets, strongly null sets, concentrated sets, perfectly meagre sets, σ-sets, γ-sets, sets with the Menger, the Rothberger, or the Hurewicz property, but also of some less-know classes like X-small sets, meagre additive sets, Ramsey null sets, Marczewski, Silver, Miller, and Laver-null sets. We notice that many classical theorems regarding these classes can be relatively easy generalized to higher cardinals although sometimes with some additional assumptions. This paper serves as a catalogue of such results along with some other generalizations and open problems.

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“…We conclude this section with a few remarks on meager-additive sets in the The question whether E-additive sets are related to M-additive sets are related was posed by Nowik and Weiss [34]. Their question was answered in [54] by the following theorem.…”

Section: Meager Additive Sets and Sharp Measure Zeromentioning

confidence: 99%