TY - JOUR
T1 - A model with no magic set
AU - Ciesielski, Krzysztof
AU - Shelah, Saharon
PY - 1999/12
Y1 - 1999/12
N2 - We will prove that there exists a model of ZFC+"c = ω2" in which every M ⊆ ℝ of cardinality less than continuum c is meager, and such that for every X ⊆ ℝ of cardinality c there exists a continuous function f : ℝ → ℝ with f[X] = [0, 1]. In particular in this model there is no magic set, i.e., a set M ⊆ ℝ such that the equation f[M] = g[M] implies f = g for every continuous nowhere constant functions f, g : ℝ → ℝ.
AB - We will prove that there exists a model of ZFC+"c = ω2" in which every M ⊆ ℝ of cardinality less than continuum c is meager, and such that for every X ⊆ ℝ of cardinality c there exists a continuous function f : ℝ → ℝ with f[X] = [0, 1]. In particular in this model there is no magic set, i.e., a set M ⊆ ℝ such that the equation f[M] = g[M] implies f = g for every continuous nowhere constant functions f, g : ℝ → ℝ.
UR - http://www.scopus.com/inward/record.url?scp=0033261212&partnerID=8YFLogxK
U2 - 10.2307/2586790
DO - 10.2307/2586790
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AN - SCOPUS:0033261212
SN - 0022-4812
VL - 64
SP - 1467
EP - 1490
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 4
ER -