Indiscernibles
In mathematical logic, indiscernibles are objects that cannot be distinguished by any property or relation defined by a formula. Usually only first-order formulas without equality are considered.
Examples
If a, b, and c are distinct and is a set of indiscernibles, then, for example, for each binary formula, we must haveHistorically, the identity of indiscernibles was one of the laws of thought of Gottfried Leibniz.
Generalizations
In some contexts one considers the more general notion of order-indiscernibles, and the term sequence of indiscernibles often refers implicitly to this weaker notion. In our example of binary formulas, to say that the triple of distinct elements is a sequence of indiscernibles impliesMore generally, for a structure with domain and a linear ordering, a set is said to be a set of -indiscernibles for if for any finite subsets and with and and any first-order formula of the language of with free variables,.p. 2