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 followin...

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Veröffentlicht in:arXiv.org 2020-09
Hauptverfasser: Khomskii, Yurii, Koelbing, Marlene, Laguzzi, Giorgio, Wohofsky, Wolfgang
Format: Artikel
Sprache:eng
Schlagworte:
Continuity (mathematics)
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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^{
ISSN:2331-8422