Shelah-Stupp’s Iteration and Muchnik’s Iteration

• Published in: Fundamenta informaticae Vol. 159; no. 4; pp. 327 - 359
• Main Authors: Caucal, Didier, Knapik, Teodor
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2018; IOS Press BV; Polskie Towarzystwo Matematyczne
• Subjects: Computer Science; Construction; Formal Languages and Automata Theory; Hierarchies; Iterative methods; Logic in Computer Science; Shelah-Stupp’s iteration; structure-building operations; Muchnik’s iteration; infinite-state systems; Shelah-Stupp's iteration; Muchnik's iteration

In the early seventies, Shelah proposed a model-theoretic construction, nowadays called “iteration”. This construction is an infinite replication in a tree-like manner where every vertex possesses its own copy of the original structure. Stupp proved that the decidability of the monadic second-order...