A simple continuous theory

Journal of Mathematical Logic (forthcoming)
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Abstract

Journal of Mathematical Logic, Ahead of Print. 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 [math]-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.

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