Inclusion modulo nonstationary

Joint work with Gabriel Fernandes and Miguel Moreno.

Abstract. A classical theorem of Hechler asserts that the structure (ωω,) is universal in the sense that for any σ-directed poset P with no maximal element, there is a ccc forcing extension in which (ωω,) contains a cofinal order-isomorphic copy of P.

In this paper, we prove a consistency result concerning the universality of the higher analogue (κκ,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 κκ and every stationary subset S of κ, there is a Lipschitz map reducing Q to (κκ,S).

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Citation information:

G. Fernandes, M. Moreno and A. Rinot, Inclusion modulo nonstationary, Monatsh. Math., 192(4): 827-851, 2020.

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One Response to Inclusion modulo nonstationary

  1. saf says:

    Submitted to Monatshefte für Mathematik, June 2019.
    Accepted, May 2020.

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