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- W131676065 abstract "Define (*) There exists $(phi_n:omega_1to omega_1:n<omega)$ such that for every uncountable $I$ which is a subset of $omega_1$ there exists $n$ such that $phi_n$ maps $I$ onto $omega_1$. This is roughly what Sierpinski in his book on the continuum hypothesis refers to as $P_3$ but I think he brings reals number line into it. I don't know French so I cannot say for sure what he says but I think he proves that (*) follows from the continuum hypothesis. We show that the existence of a Luzin set implies (*); and (*) implies that there exists a nonmeager set of reals of size $omega_1$. We also show that it is relatively consistent that (*) holds but there is no Luzin set. All the other properties in this paper, (**), (S*), (S**), (B*) are shown to be equivalent to (*)." @default.
- W131676065 created "2016-06-24" @default.
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- W131676065 date "2014-08-12" @default.
- W131676065 modified "2023-09-27" @default.
- W131676065 title "The onto mapping property of Sierpinski" @default.
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