Putting a diamond inside the square

Sun, 25/01/2015 - 10:15
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Gray's combinatorial principle SD_k is a strong combination of Jensen's Square_k and Diamond(k^+) principles. This principle proved itself very useful in constructing uncountable graphs of counter-intuitive nature.

By a 35 year old theorem of Shelah, Square_k+Diamond(k^+) does not imply SD_k for regular uncountable cardinals k. In this talk, I will prove that they are equivalent whenever k is singular.

 

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