Knaster's condition

In mathematics, a partially ordered set P is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset A of P has an upwards-linked uncountable subset. An analogous definition applies to Knaster's condition downwards. The property is named after Polish mathematician Bronisław Knaster. Furthermore, assuming MA, ccc implies Knaster's condition, making the two equivalent.

Knaster's condition

In mathematics, a partially ordered set P is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset A of P has an upwards-linked uncountable subset. An analogous definition applies to Knaster's condition downwards. The property is named after Polish mathematician Bronisław Knaster. Furthermore, assuming MA, ccc implies Knaster's condition, making the two equivalent.