Asset Details
Do you wish to reserve the book?
The Ramsey property implies no mad families
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
The Ramsey property implies no mad families
Do you wish to request the book?
The Ramsey property implies no mad families
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
The Ramsey property implies no mad families
2019
Overview
We show that if all collections of infinite subsets of ℕ have the Ramsey property, then there are no infinite maximal almost disjoint (mad) families. The implication is proved in Zermelo–Fraenkel set theory with only weak choice principles. This gives a positive solution to a long-standing problem that goes back to Mathias [A. R. D. Mathias, Ann. Math. Logic 12, 59–111 (1977)]. The proof exploits an idea which has its natural roots in ergodic theory, topological dynamics, and invariant descriptive set theory: We use that a certain function associated to a purported mad family is invariant under the equivalence relation E₀ and thus is constant on a “large” set. Furthermore, we announce a number of additional results about mad families relative to more complicated Borel ideals.
Publisher
National Academy of Sciences
Subject
