Inclusion modulo nonstationary

2019/06/24 by Fernandes, Gabriel, Moreno, Miguel, Rinot, Assaf
#03E35 (Primary) 03E45 #54H05 (Secondary) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1906.10066

Abstract

A classical theorem of Hechler asserts that the structure (ω^ω,≤^*) is universal in the sense that for any σ-directed poset P with no maximal element, there is a ccc forcing extension in which (ω^ω,≤^*) contains a cofinal order-isomorphic copy of P. In this paper, we prove a consistency result concerning the universality of the higher analogue (κ^κ,≤^S): Theorem. Assume GCH. For every regular uncountable cardinal κ, there is a cofinality-preserving GCH-preserving forcing extension in which for every analytic quasi-order Q over κ^κ and every stationary subset S of κ, there is a Lipschitz map reducing Q to (κ^κ,≤^S).

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