2015/08/26 by John T. Baldwin, Baldwin, John, Ioannis Souldatos +1
Computer Science · #03C15 #03C30 #03C35 Secondary 03C52 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Natural Language Processing Techniques #Primary 03C75
paper · pdf · doi:10.48550/arxiv.1508.06620
openalex publication_date 2015/08/26 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In [BKS15] examples of incomplete sentences are given with maximal models in more than one cardinality. The question was raised whether one can find similar examples of complete sentences. In this paper we give examples of complete Lω1,ω-sentences with maximal models in more than one cardinality. From (homogeneous) characterizability of κ we construct sentences with maximal models in κ and in one of κ+, κω, 2κ and more. Indeed, consistently we find sentences with maximal models in uncountably many distinct cardinalities.