variables in the formula. A set A {\displaystyle A} is definable in M {\displaystyle {\mathcal {M}}} without parameters if it is definable in M {\displaystyle...

In mathematical set theory, a set S is said to be ordinal definable if, informally, it can be defined in terms of a finite number of ordinals by a first-order...

have only countably many formulas, every notion of definable numbers has at most countably many definable real numbers. However, by Cantor's diagonal argument...

up definable in Wiktionary, the free dictionary. In mathematical logic, the word definable may refer to: A definable real number A definable set A definable...

{\displaystyle \mathbb {R} } to define a curve. In general, definable sets without quantifiers are easy to describe, while definable sets involving possibly nested...

sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton. Sets...

complicated definable equivalence relations. This has important applications to the study of invariants in many fields of mathematics. In set theory as...

In computability theory, a set of natural numbers is computable (or decidable or recursive) if there is an algorithm that computes the membership of every...

well-ordered set, usually represented by a von Neumann ordinal, a transitive set well ordered by ∈. 2.  An ordinal definable set is a set that can be defined by...

portal Mathematics portal Analytic proposition Circular definition Definable set Definitionism Denotation Extensional definition Fallacies of definition...

of only two sets. Ice Age and Alliances were the first two sets to have a well-defined relationship, but the idea of calling connected sets a "block" or...

projective sets of reals; however for reasons related to Tarski's undefinability theorem the notion of a definable set of reals cannot be defined in the language...

arithmetical property. A set Y of natural numbers is implicitly arithmetical or implicitly arithmetically definable if it is definable with an arithmetical...

and R {\displaystyle R} that defines a set of integers that is not definable using only addition. Presburger-definable relations admit another characterization:...

organizational change and performance Ordinal definable set, a set requiring only finitely-many ordinals to define under first-order logic. OD (video game)...

\Pi _{n}^{0}} formulas that define the set. For example, the set of odd natural numbers n {\displaystyle n} is definable by either ∀ k ( n ≠ 2 × k ) {\displaystyle...

tunnel information before the IPv4 client address. Thus there is no definable set of prefixes more specific than 2001:0::/32 for Teredo packets with Martian...

both the empty set both the entire set X {\displaystyle X} and is closed under countable union and countable intersection. Then we can define the Borel σ-algebra...

Skolemization Lindenbaum–Tarski algebra Löb's theorem Arithmetical set Definable set Ehrenfeucht–Fraïssé game Herbrand interpretation / Herbrand structure...

the set of all natural numbers. Other recursively defined mathematical objects include factorials, functions (e.g., recurrence relations), sets (e.g...

{M}}} is said to be definable (or explicitly definable cf. Beth definability, or ∅ {\displaystyle \emptyset } -definable, or definable with parameters from...

This is also known as set comprehension and set abstraction. Set-builder notation can be used to describe a set that is defined by a predicate, that is...

definable by language. Curry's paradox List of self–referential paradoxes Kleene–Rosser paradox List of paradoxes Löb's theorem Ordinal definable set...

equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence...

set is a generalization of an open interval in the real line. In a metric space (a set with a distance defined between every two points), an open set...

which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar...

definable relative to M; for others, only some integer sequences are. There is no systematic way to define in M itself the set of sequences definable...

called A-definable if it is contained in Sn(A); in that case A is called a set of parameters for D. A subset is called definable if it is A-definable for some...

variable and no free set variables). The set is assigned the classification Π n 1 {\displaystyle \Pi _{n}^{1}} if it is definable by a Π n 1 {\displaystyle...

The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/) is a two-dimensional set that is defined in the complex plane as the complex numbers c {\displaystyle c} for...