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• W3031682278 abstract "A classical theorem of Hechler asserts that the structure $$left( omega ^omega ,le ^*right) $$ is universal in the sense that for any $$sigma $$ -directed poset $${mathbb {P}}$$ with no maximal element, there is a ccc forcing extension in which $$left( omega ^omega ,le ^*right) $$ contains a cofinal order-isomorphic copy of $${mathbb {P}}$$ . In this paper, we prove the following consistency result concerning the universality of the higher analogue $$left( kappa ^kappa ,le ^Sright) $$ : assuming $$textsf {GCH }$$ , for every regular uncountable cardinal $$kappa $$ , there is a cofinality-preserving $$textsf {GCH }$$ -preserving forcing extension in which for every analytic quasi-order $${mathbb {Q}}$$ over $$kappa ^kappa $$ and every stationary subset S of $$kappa $$ , there is a Lipschitz map reducing $${mathbb {Q}}$$ to $$(kappa ^kappa ,le ^S)$$ ." @default.
• W3031682278 created "2020-06-05" @default.
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• W3031682278 date "2020-05-31" @default.
• W3031682278 modified "2023-09-30" @default.
• W3031682278 title "Inclusion modulo nonstationary" @default.
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• W3031682278 doi "https://doi.org/10.1007/s00605-020-01431-6" @default.
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