Statement:
Ramsey's Theorem I: If \(A\) is an infinite set and the family of all 2 element subsets of \(A\) is partitioned into 2 sets \(X\) and \(Y\), then there is an infinite subset \(B\subseteq A\) such that all 2 element subsets of \(B\) belong to \(X\) or all 2 element subsets of \(B\) belong to \(Y\). (Also, see Form 325.), Jech [1973b], p 164 prob 11.20.
Howard_Rubin_Number: 17
Parameter(s): This form does not depend on parameters
This form's transferability is: Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
Ramsey-1929: On a problem of formal logic
Book references
The Axiom of Choice, Jech, T., 1973b
Note connections: