Mathematics › Set theory
The implementation of mathematical concepts in set theory is a major facet of the formalization of mathematics. Here "set theory" is axiomatic set theory, not the naive set theory commonly used as a mathematical lingua franca.
Mathematics › Set theory
Paradox in set theory
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901.
Mathematics › Set theory
Mathematical technique used in proof theory
In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength.
Mathematics › Set theory
Theorem in set theory
In set theory, Kőnig's theorem states that if the axiom of choice holds, I is a set, κi and λi are cardinal numbers with κi<λi for every i in I, then ∑i∈Iκi<∏i∈Iλi. The sum here is the cardinality of the disjoint union of the sets, and the product is the cardinality of the Cartesian product.
Mathematics › Set theory
Proposition in mathematical logic
In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) 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.
Mathematics › Set theory
Possible axiom for set theory
In mathematics, 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 topological games of length ω.
Mathematics › Set theory
Mathematical function on ordinals
In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced by Oswald Veblen in Veblen (1908).
Mathematics › Set theory
Function that returns cardinal numbers
In mathematics, a cardinal function (or cardinal invariant) is a function that returns cardinal numbers.
Mathematics › Set theory
Number that is larger than all finite numbers
In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers.
Mathematics › Set theory
Order type of the set of all recursive ordinals
In mathematics, particularly set theory, non-recursive ordinals are large countable ordinals greater than all the recursive ordinals, and therefore can not be expressed using recursive ordinal notations.
Mathematics › Set theory
1960 mathematics textbook by Paul Halmos
Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. Originally published by Van Nostrand in 1960, it was reprinted in the Springer-Verlag Undergraduate Texts in Mathematics series in 1974.
Mathematics › Set theory
Public clock in Berlin, Germany
The Mengenlehreuhr (German for "Set Theory Clock") or Berlin-Uhr ("Berlin Clock") is the first public clock in the world that tells the time by means of illuminated, coloured fields, for which it entered the Guinness Book of Records upon its installation on 17 June 1975.
