A similar notion (at least in spirit) was introduced by *Simon Henry* in [**An abstract elementary class non-axiomatizable in $L_{(\infty,\kappa)}$**][1], see **Def. 4.2** and later used by *Michael Lieberman, Jiří Rosický, Sebastien Vasey* in **[Hilbert spaces and C∗-algebras are not finitely concrete.][2]**


  [1]: https://arxiv.org/abs/1812.00652
  [2]: https://arxiv.org/abs/1908.10200