Logic and Set Theory: Sigma_1-partition properties

14 February 2017, 3.00 PM - 14 February 2017, 4.30 PM

Philipp Luecke Hausdorff Center, University of Bonn

Howard House 4th Floor Seminar Room

Sigma_1-partition properties

We consider colourings of the set of pairs of countable ordinals with two colours that are definable by Sigma_1-formulas that only use the first uncountable cardinal omega_1 and real numbers as parameters. We present results showing that the existence of a measurable cardinal above a Woodin cardinal implies that uncountable homogeneous sets exist for all such colourings. In contrast, a failure of this partition property is compatible with the existence of a single Woodin cardinal. Finally, we show that similar definable partition properties can hold for large cardinals that are not weakly compact;  e.g. stationary limits of omega_1-iterable cardinals.

Contact information

p.welch@bristol.ac.uk

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