Laver Trees in the Generalized Baire Space

Laver Trees in the Generalized Baire Space

We prove that any suitable generalization of Laver forcing to the space $ \kappa^\kappa$, for uncountable regular $\kappa$, necessarily adds a Cohen $\kappa$-real. We also study a dichotomy and an ideal naturally related to generalized Laver forcing. Using this dichotomy, we prove the following stro...

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Hauptverfasser: Khomskii, Yurii, Koelbing, Marlene, Laguzzi, Giorgio, Wohofsky, Wolfgang
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Logic
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Zusammenfassung:We prove that any suitable generalization of Laver forcing to the space $ \kappa^\kappa$, for uncountable regular $\kappa$, necessarily adds a Cohen $\kappa$-real. We also study a dichotomy and an ideal naturally related to generalized Laver forcing. Using this dichotomy, we prove the following stronger result: if $ \kappa^{
DOI:10.48550/arxiv.2009.01886