Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of nonempty sets is nonempty. Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite. Formally, it states that for every indexed family of nonempty sets there exists an indexed family of elements such that for every . The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the wellordering theorem.
 Continuum hypothesis

In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. It states:There is no set whose cardinality is strictly between that of the integers and the real numbers
 Axiom schema of replacement
 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. It is necessary for the construction of certain infinite sets in
 Definable real number
 Informally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language. For example, the positive square root of 2, , can be defined
 Wellorder
 In mathematics, a wellorder on a set S is a total order on S with the property that every nonempty subset of S has a least element in this ordering. The set S together with the wellorder relation is then called a wellordered set. In some academic
 Axiom of countable choice
 The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of nonempty sets must have a choice function. That is, given a function A with domain N such that A(n) is a
 Inaccessible cardinal
 In set theory, an uncountable cardinal is inaccessible if it cannot be obtained from smaller cardinals by the usual operations of cardinal arithmetic. More precisely, a cardinal κ is strongly inaccessible if it is uncountable, it is not a sum of fewer
 Compact space
 In mathematics, specifically general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed and bounded.
Examples of compact spaces include a closed real interval, a union of a finite number of closed
 Boolean prime ideal theorem
 In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement for filters on sets is known as the ultrafilter lemma. Other theorems are obtained by considering
 Zermelo–Fraenkel set theory
 In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's
 Robert Grierson (missionary)
 Robert G. Grierson was a Canadian medical doctor, Presbyterian missionary, and educator who worked in Korea for thirtysix years. He is also known by his Korean name, 구례선. Grierson performed his missionary works in the Sungjin and Hamheung area