Non-special Aronszajn trees on ℵω+1 |
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Authors: | Shai Ben-David Saharon Shelah |
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Institution: | (1) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel |
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Abstract: | We continue our research on the relative strength ofL-like combinatorial principles for successors of singular cardinals. In 3] we have shown that the existence of a λ+-special Aronszajn tree does not follow from that of a λ+-Souslin tree. It follows from 5], 4] and 6] that under G.C.H. □λ does imply the existence of a λ+-Souslin tree. In 2] we show that □λ does not follow from the existence of a λ+-special Aronszajn tree. Here we show that the existence of such a tree implies that of an ‘almost Souslin’ λ+-tree. It follows that the statement “All λ+-Aronszajn trees are special” implies that there are no λ+-Aronszajn trees. |
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