Editing Combinatorics (section)

===Infinitary combinatorics===
{{Main|Infinitary combinatorics}}

Infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets.  It is a part of [[set theory]], an area of [[mathematical logic]], but uses tools and ideas from both set theory and extremal combinatorics. Some of the things studied include [[continuous graph]]s and [[Tree (set theory)|trees]], extensions of [[Ramsey's theorem]], and [[Martin's axiom]]. Recent developments concern combinatorics of the [[Continuum (set theory)|continuum]]<ref>[[Andreas Blass]], ''Combinatorial Cardinal Characteristics of the Continuum'', Chapter 6 in Handbook of Set Theory, edited by [[Matthew Foreman]] and [[Akihiro Kanamori]], Springer, 2010</ref> and combinatorics on successors of singular cardinals.<ref>{{Citation |last=Eisworth |first=Todd |title=Successors of Singular Cardinals |date=2010 |url=http://link.springer.com/10.1007/978-1-4020-5764-9_16 |work=Handbook of Set Theory |pages=1229–1350 |editor-last=Foreman |editor-first=Matthew |place=Dordrecht |publisher=Springer Netherlands |language=en |doi=10.1007/978-1-4020-5764-9_16 |isbn=978-1-4020-4843-2 |access-date=2022-08-27 |editor2-last=Kanamori |editor2-first=Akihiro}}</ref>

[[Gian-Carlo Rota]] used the name ''continuous combinatorics''<ref>{{Cite web |url=http://faculty.uml.edu/dklain/cpc.pdf |title=''Continuous and profinite combinatorics'' |access-date=2009-01-03 |archive-date=2009-02-26 |archive-url=https://web.archive.org/web/20090226040144/http://faculty.uml.edu/dklain/cpc.pdf |url-status=live }}</ref> to describe [[geometric probability]], since there are many analogies between ''counting'' and ''measure''.