SQUARE WITH BUILT-IN DIAMOND-PLUS
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AbstractWe formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds inLfor every infinite cardinal.As an application, we prove that the following two hold inL:1.For every infinite regular cardinalλ, there exists a special λ+-Aronszajn tree whose projection is almost Souslin;2.For every infinite cardinalλ, there exists arespectingλ+-Kurepa tree; Roughly speaking, this means that this λ+-Kurepa tree looks very much like the λ+-Souslin trees that Jensen constructed inL.
1994 ◽
Vol 144
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pp. 431-434
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1979 ◽
Vol 44
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pp. 357-372
Keyword(s):
1977 ◽
Vol 35
◽
pp. 210-211
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1970 ◽
Vol 28
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pp. 542-543
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1967 ◽
Vol 25
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pp. 170-171