I am computer scientist, not a mathematician, I've been reading some papers on argumentation in AI that uses the term 'maximal' set without defining it. I think it's left undefined because it's a term used widely in mathematics? The paper at the end of this post. I hope this question isn't too simple for this forum and I hope set theory is ok as a tag?!

Many thanks.

@article{Dung2007642, title = "Computing ideal sceptical argumentation", journal = "Artificial Intelligence", volume = "171", number = "10-15", pages = "642 - 674", year = "2007", note = "Argumentation in Artificial Intelligence", doi = "DOI: 10.1016/j.artint.2007.05.003", author = "P.M. Dung and P. Mancarella and F. Toni" }