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  2. Cardinality (data modeling) - Wikipedia

    en.wikipedia.org/wiki/Cardinality_(data_modeling)

    Within data modelling, cardinality is the numerical relationship between rows of one table and rows in another. Common cardinalities include one-to-one , one-to-many , and many-to-many . Cardinality can be used to define data models as well as analyze entities within datasets.

  3. One-to-many (data model) - Wikipedia

    en.wikipedia.org/wiki/One-to-many_(data_model)

    In systems analysis, a one-to-many relationship is a type of cardinality that refers to the relationship between two entities (see also entity–relationship model). For example, take a car and an owner of the car. The car can only be owned by one owner at a time or not owned at all, and an owner could own zero, one, or multiple cars.

  4. One-to-one (data model) - Wikipedia

    en.wikipedia.org/wiki/One-to-one_(data_model)

    A country has only one capital city, and a capital city is the capital of only one country. (Not valid for some countries).. In systems analysis, a one-to-one relationship is a type of cardinality that refers to the relationship between two entities (see also entity–relationship model) A and B in which one element of A may only be linked to one element of B, and vice versa.

  5. Many-to-many (data model) - Wikipedia

    en.wikipedia.org/wiki/Many-to-many_(data_model)

    For example, think of A as Authors, and B as Books. An Author can write several Books, and a Book can be written by several Authors. In a relational database management system, such relationships are usually implemented by means of an associative table (also known as join table, junction table or cross-reference table), say, AB with two one-to-many relationships A → AB and B → AB.

  6. Cardinality - Wikipedia

    en.wikipedia.org/wiki/Cardinality

    The cardinality of the natural numbers is denoted aleph-null (), while the cardinality of the real numbers is denoted by "" (a lowercase fraktur script "c"), and is also referred to as the cardinality of the continuum.

  7. Categorical theory - Wikipedia

    en.wikipedia.org/wiki/Categorical_theory

    A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley stating that if a first-order theory in a countable language is categorical in some uncountable cardinality, then it is categorical in all uncountable cardinalities.

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  9. Saturated model - Wikipedia

    en.wikipedia.org/wiki/Saturated_model

    This can be generalized as follows: the unique model of cardinality κ of a countable κ-categorical theory is saturated. However, the statement that every model has a saturated elementary extension is not provable in ZFC. In fact, this statement is equivalent to [citation needed] the existence of a proper class of cardinals κ such that κ <κ ...