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11 relations: Cardinal number, Equiconsistency, Homogeneous (large cardinal property), Large cardinal, List of large cardinal properties, Mathematics, Power set, Remarkable cardinal, Stationary set, Subtle cardinal, Transfinite number.
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.
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Equiconsistency
In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa.
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Homogeneous (large cardinal property)
In set theory and in the context of a large cardinal property, a subset, S, of D is homogeneous for a function f if for some natural number n, \mathcal_(D) (see Powerset#Subsets of limited cardinality) is the domain of f and for some element r of the range of f, every member of \mathcal_(S) is mapped to r. That is, f is constant on the unordered n-tuples of elements of S.
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Large cardinal
In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.
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List of large cardinal properties
This page includes a list of cardinals with large cardinal properties.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Power set
In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
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Remarkable cardinal
In mathematics, a remarkable cardinal is a certain kind of large cardinal number.
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Stationary set
In mathematical set theory and model theory, a stationary set is one that is not too small in the sense that it intersects all club sets, and is analogous to a set of non-zero measure in set theory.
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Subtle cardinal
In mathematics, subtle cardinals and ethereal cardinals are closely related kinds of large cardinal number.
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Transfinite number
Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite.
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Almost ineffable cardinal, Totally ineffable cardinal.
