I gave an invited talk at the 120 Years of Choice conference, July 2024.
Talk Title: Mathematician’s best friend
Abstract: Jensen’s diamond is a very useful postulate. It is well-known that it implies the continuum hypothesis, that it is equivalent to seemingly weaker forms in which the frequency of guesses is not imposed to be stationary or in which the number of candidates for a guess at each level is bigger than one, and that many sincerely weak forms of diamond are still refuted by forcing axioms.
In this talk, we will consider variations of the original diamond that enable to challenge these four well-known facts. As an application, an affirmative answer to a question of Leiderman and Szeptycki (concerning countably metacompact topological spaces) will be given.
This is joint work with Rodrigo Carvalho, Tanmany Inamdar, Ziemek Kostana and Saharon Shelah.
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