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math.LO2026
Nonembeddings of Combinatory Algebras
Patrick Lutz, Paul Shafer, Sebastiaan A. Terwijn
In the theory of combinatorial algebras, there is a sequence of embeddings between Kleene's second model, van Oosten's model, and Scott's graph model. We prove that none of these e…
math.LO2023
A Note on a Conjecture of Sacks: It is Harder to Embed Height Three Partial Orders than Height Two Partial Orders
Kojiro Higuchi, Patrick Lutz
A long-standing conjecture of Sacks states that it is provable in ZFC that every locally countable partial order of size continuum embeds into the Turing degrees. We show that this…