---
tag: B3XW32T6EH
kind: concept
name: Hrushovski construction
sources:
  - wikipedia: en:18926594@r1298784173
    locator: Hrushovski construction
    note: adopted
    mention: wikipedia://en/18926594
    sections: [Summary]
same_as:
  wikidata: Q5923924
  wikipedia: Hrushovski construction
inventory: [21958AHGYT]
---

## Summary

In model theory, a branch of mathematical logic, the **Hrushovski construction** generalizes the Fraïssé limit by working with a notion of *strong substructure* $\leq$ rather than $\subseteq$. It can be thought of as a kind of "model-theoretic forcing", where a (usually) stable structure is created, called the *generic* or *rich*  model. The specifics of $\leq$ determine various properties of the generic, with its geometric properties being of particular interest. It was initially used by Ehud Hrushovski to generate a stable structure with an "exotic" geometry, thereby refuting Zil'ber's Conjecture.