| Résume | Many definable subsets of the Baire space of functions on the natural numbers satisfy the Baire property, for instance all analytic sets. However, it is well known that some simply definable subsets of the space of functions on a regular uncountable cardinal fail to satisfy the analogue to the Baire property. We introduce a more general property that is equal to the Baire property in the countable setting, and show that it is consistent that all definable subsets of the space of functions on an uncountable regular cardinal have this property. We consider applications such as the non-existence of definable well-orders. |
