Arithmetical Complexity and Absoluteness of Rigidity Phenomena for Ulam Sequences

2025/11/17 by Frank Gilson, Gilson, Frank
Computer Science · Mathematics · #11B83 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2511.13066

openalex publication_date 2025/11/17 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28

Abstract

We analyse the logical complexity and absoluteness of natural statements about Ulam sequences, with particular emphasis on the rigidity phenomena introduced by Hinman, Kuca, Schlesinger and Sheydvasser for the family U(1,n). For each pair of coprime integers a<b></b>

Citations

• Ulam Sequences and Ulam Sets
• A Hidden Signal in the Ulam sequence
• Vapnik-Chervonenkis density in some theories without the independence property, I

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• The Unreasonable Rigidity of Ulam Sets
• The Ulam Sequence of the Integer Polynomial Ring
• Ulam Sequences and Ulam Sets
• Rigidity sequences, Kazhdan sets and group topologies on the integers
• Small gaps in the Ulam sequence