Large Cardinal Axiom
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Large cardinal property — In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very large (for example, bigger than aleph zero … Wikipedia
List of large cardinal properties — This page is a list of some types of cardinals; it is arranged roughly in order of the consistency strength of the axiom asserting the existence of cardinals with the given property. Existence of a cardinal number κ of a given type implies the… … Wikipedia
Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of … Wikipedia
Axiom of constructibility — The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written as : V = L , where V and L denote the von Neumann universe and the constructible universe,… … Wikipedia
Axiom of infinity — In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of infinity is one of the axioms of Zermelo Fraenkel set theory. Formal statement In the formal language of the Zermelo Fraenkel axioms,… … Wikipedia
Cardinal number — This article describes cardinal numbers in mathematics. For cardinals in linguistics, see Names of numbers in English. In mathematics, cardinal numbers, or cardinals for short, are generalized numbers used to measure the cardinality (size) of… … Wikipedia
Axiom of determinacy — The axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two person games of length ω with perfect information. AD states that every such game in… … Wikipedia
Large countable ordinal — In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of… … Wikipedia
Axiom of projective determinacy — In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets. The axiom of projective determinacy, abbreviated PD, states that for any two player game of perfect information of… … Wikipedia
Axiom of real determinacy — In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following::Consider infinite two person games with perfect information. Then, every game of length ω where both players choose real… … Wikipedia
Inaccessible cardinal — In set theory, an uncountable regular cardinal number is called weakly inaccessible if it is a weak limit cardinal, and strongly inaccessible, or just inaccessible, if it is a strong limit cardinal. Some authors do not require weakly and strongly … Wikipedia
