Forcing Over a Free Suslin Tree

2024/01/31 by John Krueger, Šárka Stejskalová, Krueger, John +1 · 2 citations
Computer Science · #Model-Driven Software Engineering Techniques #Natural Language Processing Techniques

paper · pdf · doi:10.48550/arxiv.2402.00226

Abstract

We introduce a forcing for adding almost disjoint automorphisms of a normal infinitely splitting ω₁-tree T with countable approximations. Assuming that T is a free Suslin tree, this forcing is totally proper, preserves the Suslinness of T, and does not add new cofinal branches of ω₁-trees existing in intermediate extensions. If κ is an inaccessible cardinal, then the product of the automorphism forcing of length κ with the Lévy collapse of κ to become ω₂ forces that there exists an almost Kurepa Suslin tree and there does not exist a Kurepa tree. This model solves open problems due to Bilaniuk, Jin, Shelah, and Moore.

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• A virtual five element basis for the uncountable linear orders
• A Strongly Non-Saturated Aronszajn Tree Without Weak Kurepa Trees

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