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

1997/06/15 by Mariusz Rabus, Saharon Shelah, Rabus, Mariusz +1
Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/9706223

published as Ann. Pure Appl. Logic 103 No. 1-3 (2000) 229--240

arxiv created 1997/06/15 · openalex publication_date 1997/06/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is consistent that for every function f:R x R-> R there is an uncountable set A subseteq R and two continuous functions f₀,f₁:D(A)-> R such that f(alpha, beta) in f₀(alpha, beta),f₁(alpha, beta) for every (alpha, beta) in A², alpha not = beta .

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