Year: 2024
Type: article
Abstract: 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 [Formula: see text]-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.
Source: Journal of Mathematical Logic
Author: James E. Hanson
Institution: Iowa State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4401821917