Productivity of maximal eventually different families

Mathematics > Logic [Submitted on 16 Jun 2026] Title:Productivity of maximal eventually different families View PDF HTML (experimental)Abstract:A maximal eventually different family is called $n$-productive if the product family $\mathcal{F}^n$ is still maximal. We construct closed $n$-productive families separating these strengthenings of maximality at every $n \geq 1$. Furthermore, we show how to force and construct an even stronger type of $\mathcal{I}_0$-productive family and discuss the relation of productivity to Van Douwen families. References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.