Abstract
We shall prove some unconnected theorems: (1) (G.C.H.) \omega _{\alpha + 1} \to \left( {\omega _\alpha + \xi } \right)_2^2 when אα is regular, {box drawings light vertical}ξ{box drawings light vertical}+<ωα. (2) There is a Jonsson algebra in אα+n, and \aleph _{a + n} \not \to \left[ {\aleph _{a + n} } \right]_{\aleph _{a + n} }^{n + 1} if 2^{\aleph _{ - - } } = \aleph _{a + n} \cdot (3) If λ>א0 is a strong limit cardinal, then among the graphs with ≦λ vertices each of valence <λ there is a universal one. (4)(G.C.H.) If f is a set mapping on \omega _{a + 1} (אα regular) {box drawings light vertical}f(x)∩f(y{box drawings light vertical}<אα, then there is a free subset of order-type ζ for every ζ<ωα+1.
Original language | English |
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Pages (from-to) | 262-277 |
Number of pages | 16 |
Journal | Israel Journal of Mathematics |
Volume | 14 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1973 |