2020/03/28 by Sean Cox, Cox, Sean
Computer Science · #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2003.12692
openalex publication_date 2020/03/28 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Fuchino-Maschio-Sakai~\citeFuchinoEtAlDRPLST proved that the Löwenheim-Skolem-Tarski (LST) property of Stationary Logic is equivalent to the Diagonal Reflection Principle on internally club sets (DRPIC) introduced in \citeDRP. We prove that the restriction of the LST property to (downward) reflection of Π11 formulas, which we call the Π11 \downarrow-LST property, is equivalent to the internal version of DRP from \citeCoxRPIS. Combined with results from \citeCoxRPIS, this shows that the Π11 \downarrow-LST Property for Stationary Logic is strictly weaker than the full LST Property for Stationary Logic, though if CH holds they are equivalent.