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请输入英文单字，中文词皆可：

definable    音标拼音: [dɪf'ɑɪnəbəl]
a. 可解说的,可下定义的,可解释的

可解说的,可下定义的,可解释的

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  • model theory - How to prove that something is definable or not . . .
    And for example $\mathbb {Z}$ is definable in $\mathbb {Q}$, so an argument based on roots of polynomials is unlikely to be enough For a good understanding of definability in $\mathbb {R}$, the fact that the definable subsets are simple combinations of semi-algebraic sets is the key result, and in a sense undecidability is peripheral
  • Difference definable vs. computable - Mathematics Stack Exchange
    A definable number requires a statement which uniquely identifies it Any computable number is definable since its program can serve as its definition A number which is definable but not computable is necessarily fairly weird One example is: Chaitin's Constant This relies on something called the Halting Problem
  • What is definability in First-Order Logic? - Mathematics Stack Exchange
    Informally, a definable subset of $\mathbb {N}$ is a set completely specifiable by a formula in our formal language Ditto for subsets of $\mathbb {N}^2$ (binary relations), of $\mathbb {N}^3$, and so on
  • Definable with parameters (Example) - Mathematics Stack Exchange
    Throughout my course in Logic, I have not yet encountered a set that is definable with parameters (Most of the examples are definable without parameters) Is there a simple example of a set that is
  • set theory - What is the meaning of definable class? - Mathematics . . .
    A definable set is a definable set by first-order language in $ZFC$ because we don't care about the meta theory And so universe $V$ is a set or a formula, etc in meta-theory, however, classes including $V$, $L$, and so on are treated like set in $ZFC$
  • logic - What is a definable set? - Mathematics Stack Exchange
    You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
  • model theory - Definable types - Mathematics Stack Exchange
    You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
  • Terminology question regarding $L$ and definable real numbers
    We would like to say there are only countably many definable real numbers, except ZFC can't prove what definability is On the other hand, the cardinality of $\Bbb R \cap L$ depends on things like the existence of $0^\#$ Is ZFC, perhaps augmented with some suitable large cardinal axiom, strong enough to say anything at all about this?
  • Is there a known well ordering of the reals?
    The stronger hypothesis of "projective determinacy" implies there is no well ordering of the reals definable by a formula in the projective hierarchy This is consistent with ZFC but not provable in ZFC Worse, it's even consistent with ZFC that no formula in the language of set theory defines a well ordering of the reals (even though one exists)
  • computability - Example of uncomputable but definable number . . .
    Every computable number is definable However, the converse is not true What is an example of a real number that is definable but that is NOT computable? I guess if it is there, we can "define" (





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