Combinatorics in Zfc Limbo
نویسنده
چکیده
In their paper, Large-scale regularities of lattice embeddings of posets [RW99], Remmel and Williamson studied extremal properties of posets and their incomparability graphs on N k . Properties (1) through (3) of their main result, Theorem 1.5, are proved using Ramsey theory. The proof of Theorem 1.5 (4), however, uses Friedman’s Jump Free Theorem ([Fri97] and [Fri98] ), a powerful ZFC independent extension of Ramsey theory. Attempts to prove Theorem 1.5 (4) within the ZFC axioms have thus far failed. This leaves the main result of [RW99] in what we informally call “ZFC limbo.” In this paper we explore other results of this type.
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تاریخ انتشار 2018