A model $M$ is <aleph-zero-homogeneous model> when, for finite tuples $\bar a,\bar b$ with the same complete type and every $c\in M$, there is $d\in M$ such that
$$
\operatorname{tp}(\bar a,c)=\operatorname{tp}(\bar b,d).
$$
Equivalently, every finite partial elementary map extends by one more element.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 144 / 3 / a / Solution

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{wiki=Homogeneous_structure}

A model is aleph-zero-homogeneous when every finite partial elementary map extends by one more element.


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