Aleksander Cieślak: Antichain numbers and other cardinal invariants of ideals
19/12/23 08:33
Tuesday, December 19, 2023 17:00
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Aleksander Cieślak
Title: Antichain numbers and other cardinal invariants of ideals
Abstract: Suppose that \(J\) is an ideal on \(\omega\). The \(J\)-antichain number is the smallest cardinality of a maximal antichain in the algebra \(P(\omega)\) modulo \(J\). We will estimate the \(J\)-antichain numbers for various Borel ideals. To do so, we will focus on two features of ideals which are crucial for our construction. First one is a cardinal invariant of an ideal \(J\) which lies (strictly) in between \(\rm{add}^*(J)\) and \(\rm{cov}^*(J)\). The second one is a property which allows diagonalisation of antichains and which is similar (but not equal) to being a \(P^+\) ideal.
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Aleksander Cieślak
Title: Antichain numbers and other cardinal invariants of ideals
Abstract: Suppose that \(J\) is an ideal on \(\omega\). The \(J\)-antichain number is the smallest cardinality of a maximal antichain in the algebra \(P(\omega)\) modulo \(J\). We will estimate the \(J\)-antichain numbers for various Borel ideals. To do so, we will focus on two features of ideals which are crucial for our construction. First one is a cardinal invariant of an ideal \(J\) which lies (strictly) in between \(\rm{add}^*(J)\) and \(\rm{cov}^*(J)\). The second one is a property which allows diagonalisation of antichains and which is similar (but not equal) to being a \(P^+\) ideal.