Definable
Definable In mathematics, a mathematical object X of some type T is definable, if there exists some predicate P(x ... X ≠ Y. All computable objects are definable, but not all definable objects are computable. Thus, we have definable numbers, definable sets , definable sequences , definable ...
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Definable number
Definable number A real number a is first-order definable in the language of set theory, without ... article, such reals will be called simply definable numbers. This should not be understood to be standard terminology. General facts The definable numbers form a field containing all the ... numbers). However, most real numbers are not definable: the set of all definable numbers ...
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Talk:Definable number
Talk:Definable number Berry's paradox, definability of definability ... whole page. If you nail down what "definable" means, you'll find that the set of definable reals itself is not definable in that sense. "Definable" is a moving target; the whole ...
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Talk:Computable number
... describable by some ZFC formula are the definable numbers. But the countablility proofs can be ... and which is not sufficiently clear in definable number) is the following: So one can ... of an enumeration of the set of definable numbers, say by lexicographically ordering the corresponding ... applied to this enumeration to determine another definable number?-- 80.136.136.219 23:41 ... but the new number won't be definable in the same sense. The set ...
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O-minimality
... M = (<,...) of T, and every set X definable (with parameters) in M, X can be ... an "interval." In other words, any set definable in M by an arbitrary formula is also definable using nothing but the ordering. In strong minimality the definable sets are precisely those definable by equality. Examples of o-minimal ...
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Talk:Eugenics
... discussion, that improvement is not a scientifically definable term. (Such programs are considered by eugenicists ... modern scholarship "disability" isn't a scientifically definable quality, so his statement fails an important ... wouldn't argue that disability is "scientifically definable". So, i'm not sure what you ... the notion of "defects" may be socially definable but not scientifically." 1. Genetic disorders are scientifically definable, e.g. Tay Sachs and Achondroplasia. ...
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Talk:Hilbert's problems
... for any property, not just first-order definable ones, so the complexity of the formula ... implies definability, and the existence of a definable wellordering of R is independent of ZFC ... reason stated above Solved negatively, because no definable wellordering can be proved to be a ... have wanted something much better than just "definable"; he would have expected something definable in some natural combinatorial way, and ...
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Talk:Cantor's diagonal argument/Archive1
... you are going. You are talking about definable numbers, and indeed there are only countably ... of them. You want to list the definable numbers in proper order (maybe lexicographically ordered ... Cantor does. So you have a new definable number which is not in your original ... is not possible to nicely order the definable numbers by their defining string. Whether a ... order of your defining strings that is "definable", in other words you would need ...
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Talk:Deconstruction
... deconstruction article. If something is truly not-definable, it can't be recognized for study ... everything good, decent, and studyable must be definable. Perhaps, nothing is definable. It's not that definitions are bullshit, or that nothing is definable. A more correct statement would be that ... Thus, it's not that "nothing is definable", but rather, a definition is kind ...
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Talk:Morse–Kelley set theory
... a "property" is (actually we want one definable by a formula in the second-order ... Then "the largest inaccessible" would be a definable rank of the von Neumann hierarchy. Now ... large collections which are not necessarily all definable as predicates). That is certainly the way ... UTC) Well, I didn't necessarily mean definable predicates. More that they shouldn't be ...
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