Form equivalence class Howard-Rubin Number: 1
Statement:
Let \(P\) be a partially ordered set in which every increasing sequence has an upper bound and \(f:P\to P\) satisfies \(x \le f(f(x))\) for all \(x\in f(P) \cup \{x\in P : x\) is an upper bound for some increasing sequence in \(f(P)\}\). Then \(f\) has a fixed apex \(u\)(that is, \(\exists v\in P\), such that \(f(u) = v\) and \(f(v) = u\)). (For purposes of [1 BD], ``sequence'' means a function whose domain is an ordinal.)
Howard-Rubin number: 1 BD
Citations (articles):
Taskovi'c [1992b]
New maximal principles
Connections (notes):
References (books):
Back