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On the extendability to \(\mathbf {\Pi }_3^0\) ideals and Katětov order
We show that there is a \( \varvec{\Sigma }_4^0\) ideal such that it’s neither extendable to any \( \varvec{\Pi }_3^0\) ideal nor above the ideal \( \textrm{Fin}\times \textrm{Fin} \) in the sense of Katětov order, answering a question from M. Hrušák.
期刊介绍：
The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.
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