indiscernibles
Sign in to saveIn 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 {a, b, c} is a set of indiscernibles, then, for example, for each binary formula \beta , we must have
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Vinony's link graph records 15 inbound references to indiscernibles, and connects out to equality, Gottfried Wilhelm Leibniz and International Standard Book Number.
It is catalogued under the topic Model theory.
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- Examples
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- Applications
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- References
- Citations
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 {a, b, c} is a set of indiscernibles, then, for example, for each binary formula \beta , we must have [ \beta (a, b) \land \beta (b, a) \land \beta (a, c) \land \beta (c, a) \land \beta (b, c) \land \beta (c, b) ] \lor [ \lnot \beta (a, b) \land \lnot \beta (b, a) \land \lnot \beta(a, c) \land \lnot \beta (c, a) \land \lnot \beta (b, c) \land \lnot \beta (c, b) ] \,.
Historically, the identity of indiscernibles was one of the laws of thought of Gottfried Leibniz.
Excerpted from Wikipedia’s “indiscernibles” article, available under the CC BY-SA 4.0 licence.