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DEFINABLE
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- The Berry paradox is a self-referential paradox arising from an expression like "The smallest positive integer not definable in under sixty letters" (a phrase with fifty-seven letters).
- Informally, a definable real number is a real number that can be uniquely specified by its description.
- In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other.
- In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set.
- Wide (ecotone) – A large distance separates the borders of two clearly and purely definable habitats based upon their physical conditions and vegetation, and in between there exists a large transition region.
- The earliest courtiers coincide with the development of definable courts beyond the rudimentary entourages or retinues of rulers.
- Whether classical or constructive in some fashion, any such framework of analysis axiomatizes the real number line by some means, a collection extending the rationals and with an apartness relation definable from an asymmetric order structure.
- The term "song cycle" did not enter lexicography until 1865, in Arrey von Dommer's edition of Koch’s Musikalisches Lexikon, but works definable in retrospect as song cycles existed long before then.
- In the modern ZFC system, the "propositional function" referred to in the axiom of separation is interpreted as "any property definable by a first-order formula with parameters", so the separation axiom is replaced by an axiom schema.
- System T extends the simply typed lambda calculus with a type of natural numbers and higher-order primitive recursion; in this system all functions provably recursive in Peano arithmetic are definable.
- Or if there is a measurable cardinal, then iterating the definable powerset operation rather than the full one yields Gödel's constructible universe, L, which does not satisfy the statement "there is a measurable cardinal" (even though it contains the measurable cardinal as an ordinal).
- The implication operator is also treated differently in intuitionistic logic than classical logic; in intuitionistic logic, it is not definable using disjunction and negation.
- Finitary closure operators that generalize these two operators are studied in model theory as dcl (for definable closure) and acl (for algebraic closure).
- In bacteria, however, the analogous process (defined as "the origin of new bacterial species that occupy definable ecological niches") might be more common because bacteria are less constrained by the homogenizing effects of sexual reproduction and are prone to comparatively dramatic and rapid genetic change through horizontal gene transfer.
- Integrity constraints specific to a particular relational data base must be definable in the relational data sublanguage and storable in the catalog, not in the application programs.
- They are divided into five definable groups or job communities, with colored group rate marks designating the group to which they belong: seaman, fireman, airman, constructionman, and Hospitalman.
- In harmony with Nietzsche's critique of the subject, as something definable in terms of consciousness, Heidegger distinguished Dasein from consciousness in order to emphasize the way that "Being" shapes our entire understanding and interpretation of the world.
- The arithmetical hierarchy classifies certain sets of natural numbers that are definable in the language of Peano arithmetic.
- In a sense, his best known works – the "multiforms" and his other signature paintings – are, in essence, the same expression, albeit one of purer (or less concrete or definable, depending on the interpretation) means, which is that of the same "basic human emotions", as his earlier surrealistic mythological paintings.
- The essential distinction, similar to the concept of definable numbers, contrasts the finiteness of the domain of concepts that we can specify and discuss, with the unbounded infinity of the set of numbers; compare finitism.
- More precisely, the functions definable in λ2 are those provably total in second-order Peano arithmetic.
- It is that the individual has within him or her self vast resources for self-understanding, for altering her or his self-concept, attitudes, and self-directed behaviour—and that these resources can be tapped if only a definable climate of facilitative psychological attitudes can be provided.
- The AGM postulates are equivalent to several different conditions on the revision operator; in particular, they are equivalent to the revision operator being definable in terms of structures known as selection functions, epistemic entrenchments, systems of spheres, and preference relations.
- SO-Krom is the set of boolean queries definable with second-order formulae in conjunctive normal form such that the first-order quantifiers are universal and the quantifier-free part of the formula is in Krom form, which means that the first-order formula is a conjunction of disjunctions, and in each "disjunction" there are at most two variables.
- Stated in terms of definability, a set of reals is projective iff it is definable in the language of second-order arithmetic from some real parameter.
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