Oberseminar "Mathematische Logik" - Dr. Ziemowit Kostana

I will give a short introduction to the set theoretic principles called weak (parametrized) diamonds.
These axioms are weakenings of the classical Diamond Prinicple of Jensen with interesting consequences, like for example:

- existence of Suslin trees,

- existence of many non-order-isomorphic uncountable sets of reals,

- existence of non-uniformizable colorings of ladder systems.

I will also present an alternative formulation of parametrized diamonds,
with possible new applications.