We introduce the notion of hereditary G-compactness (with respect to interpretation). We provide a sufficient condition for a poset to not be hereditarily G-compact, which we use to show that any linear order is not hereditarily G-compact. Assuming that a long-standing conjecture about unstable NIP theories holds, this implies that an NIP theory is hereditarily G-compact if and only if it is stable (and by a result of Simon, this holds unconditionally for \(\aleph _0\)-categorical theories). We show that if G is definable over A in a hereditarily G-compact theory, then \(G^{00}_A=G^{000}_A\). We also include a brief survey of sufficient conditions for G-compactness, with particular focus on those which can be used to prove or disprove hereditary G-compactness for some (classes of) theories.

我们介绍了遗传G紧凑性的概念（相对于解释而言）。我们提供了一个足够的条件，以使姿态体不是遗传上的G紧缩，我们可以用来证明任何线性顺序都不是遗传上的G紧缩。假设长期存在关于不稳定NIP理论的猜想，这意味着NIP理论在且仅当稳定时才遗传G-紧致（并且由Simon得出，这对于\（\ aleph _0 \是无条件成立的） -分类理论）。我们表明，如果ģ是可定义的过甲在世袭G-紧凑理论，然后\（G ^ {00} _A = G ^ {000} _A \）。我们还简要概述了G紧缩的充分条件，尤其着重于可用于证明或反证某些（类）理论的遗传性G紧缩的条件。