2023/06/25 by James Hanson, Hanson, James · 1 citation
Computer Science · Mathematics · #03C45 #03C66 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2306.14324
openalex publication_date 2023/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete structures. We investigate a stronger condition that is easier to establish and use it to give an example of a strictly simple continuous theory that does not interpret any infinite discrete structures: the theory of richly branching ℝ-forests with generic binary predicates. We also give an example of a superstable theory that fails to satisfy this stronger condition but nevertheless does not interpret any infinite discrete structures.