Definable Real Number
A real number a is first-order definable in the language of set theory, without parameters, if there is a formula φ in the language of set theory, with one free variable, such that a is the unique real number such that φ(a) holds in the standard model of set theory (see Kunen 1980:153).
For the purposes of this article, such reals will be called simply definable numbers. This should not be understood to be standard terminology.
Note that this definition cannot be expressed in the language of set theory itself.
Read more about Definable Real Number: General Facts, Notion Does Not Exhaust "unambiguously Described" Numbers, Other Notions of Definability
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