Covering a function on the plane by two continuous functions on an uncountable square - the consistency

Mariusz Rabus; Saharon Shelah

doi:10.1016/S0168-0072(98)00053-0

Covering a function on the plane by two continuous functions on an uncountable square - the consistency

Mariusz Rabus^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is consistent that for every function f : R×R → R there is an uncountable set A ⊆ R and two continuous functions f₀, f₁ : D(A) → R such that f(α,β) ∈ {f₀(α,β),f₁(α,β)} for every (α,β) ∈ A²,α≠β.

Original language	English
Pages (from-to)	229-240
Number of pages	12
Journal	Annals of Pure and Applied Logic
Volume	103
Issue number	1-3
DOIs	https://doi.org/10.1016/S0168-0072(98)00053-0
State	Published - 15 May 2000

Keywords

Continuous functions
Forcing
Primary 03E35

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10.1016/S0168-0072(98)00053-0

Cite this

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abstract = "It is consistent that for every function f : R×R → R there is an uncountable set A ⊆ R and two continuous functions f0, f1 : D(A) → R such that f(α,β) ∈ \{f0(α,β),f1(α,β)\} for every (α,β) ∈ A2,α≠β.",

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N2 - It is consistent that for every function f : R×R → R there is an uncountable set A ⊆ R and two continuous functions f0, f1 : D(A) → R such that f(α,β) ∈ {f0(α,β),f1(α,β)} for every (α,β) ∈ A2,α≠β.

AB - It is consistent that for every function f : R×R → R there is an uncountable set A ⊆ R and two continuous functions f0, f1 : D(A) → R such that f(α,β) ∈ {f0(α,β),f1(α,β)} for every (α,β) ∈ A2,α≠β.

KW - Continuous functions

KW - Forcing

KW - Primary 03E35

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ER -

Covering a function on the plane by two continuous functions on an uncountable square - the consistency

Abstract

Keywords

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