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

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