Faster access than browser!
48 relations: Arithmetic, Bachmann–Howard ordinal, Church–Kleene ordinal, Computable function, Constructible universe, Countable set, Elementary equivalence, Epsilon numbers (mathematics), Feferman–Schütte ordinal, First uncountable ordinal, First-order logic, Formal system, Gaisi Takeuti, Gödel's incompleteness theorems, Gerald Sacks, Gerhard Gentzen, Goodstein's theorem, Halting problem, Hartley Rogers Jr., Impredicativity, Infimum and supremum, Kleene's O, Kleene–Brouwer order, Kripke–Platek set theory, Kurt Schütte, Large cardinal, Large Veblen ordinal, Mahlo cardinal, Oracle machine, Ordinal analysis, Ordinal arithmetic, Ordinal collapsing function, Ordinal notation, Ordinal number, Peano axioms, PostScript, Proof theory, Recursive ordinal, Regular cardinal, Second-order arithmetic, Set theory, Small Veblen ordinal, Stephen Cole Kleene, Transitive model, Turing machine, Veblen function, Zermelo set theory, Zermelo–Fraenkel set theory.
Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
New!!: Large countable ordinal and Arithmetic · See more »
Bachmann–Howard ordinal
In mathematics, the Bachmann–Howard ordinal (or Howard ordinal) is a large countable ordinal.
New!!: Large countable ordinal and Bachmann–Howard ordinal · See more »
Church–Kleene ordinal
In mathematics, the Church–Kleene ordinal, \omega^_1, named after Alonzo Church and S. C. Kleene, is a large countable ordinal.
New!!: Large countable ordinal and Church–Kleene ordinal · See more »
Computable function
Computable functions are the basic objects of study in computability theory.
New!!: Large countable ordinal and Computable function · See more »
Constructible universe
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted L, is a particular class of sets that can be described entirely in terms of simpler sets.
New!!: Large countable ordinal and Constructible universe · See more »
Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
New!!: Large countable ordinal and Countable set · See more »
Elementary equivalence
In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the same first-order σ-sentences.
New!!: Large countable ordinal and Elementary equivalence · See more »
Epsilon numbers (mathematics)
In mathematics, the epsilon numbers are a collection of transfinite numbers whose defining property is that they are fixed points of an exponential map.
New!!: Large countable ordinal and Epsilon numbers (mathematics) · See more »
Feferman–Schütte ordinal
In mathematics, the Feferman–Schütte ordinal Γ0 is a large countable ordinal.
New!!: Large countable ordinal and Feferman–Schütte ordinal · See more »
First uncountable ordinal
In mathematics, the first uncountable ordinal, traditionally denoted by ω1 or sometimes by Ω, is the smallest ordinal number that, considered as a set, is uncountable.
New!!: Large countable ordinal and First uncountable ordinal · See more »
First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
New!!: Large countable ordinal and First-order logic · See more »
Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
New!!: Large countable ordinal and Formal system · See more »
Gaisi Takeuti
was a Japanese mathematician, known for his work in proof theory.
New!!: Large countable ordinal and Gaisi Takeuti · See more »
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
New!!: Large countable ordinal and Gödel's incompleteness theorems · See more »
Gerald Sacks
Gerald Enoch Sacks (born 1933, Brooklyn) is a logician who holds a joint appointment at Harvard University as a professor of mathematical logic and the Massachusetts Institute of Technology as a professor emeritus.
New!!: Large countable ordinal and Gerald Sacks · See more »
Gerhard Gentzen
Gerhard Karl Erich Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician.
New!!: Large countable ordinal and Gerhard Gentzen · See more »
Goodstein's theorem
In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0.
New!!: Large countable ordinal and Goodstein's theorem · See more »
Halting problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.
New!!: Large countable ordinal and Halting problem · See more »
Hartley Rogers Jr.
Hartley Rogers Jr. (1926–2015) was a mathematician who worked in recursion theory, and was a professor in the Mathematics Department of the Massachusetts Institute of Technology.
New!!: Large countable ordinal and Hartley Rogers Jr. · See more »
Impredicativity
Something that is impredicative, in mathematics and logic, is a self-referencing definition.
New!!: Large countable ordinal and Impredicativity · See more »
Infimum and supremum
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.
New!!: Large countable ordinal and Infimum and supremum · See more »
Kleene's O
In set theory and computability theory, Kleene's \mathcal is a canonical subset of the natural numbers when regarded as ordinal notations.
New!!: Large countable ordinal and Kleene's O · See more »
Kleene–Brouwer order
In descriptive set theory, the Kleene–Brouwer order or Lusin–Sierpiński order is a linear order on finite sequences over some linearly ordered set (X,, that differs from the more commonly used lexicographic order in how it handles the case when one sequence is a prefix of the other. In the Kleene–Brouwer order, the prefix is later than the longer sequence containing it, rather than earlier. The Kleene–Brouwer order generalizes the notion of a postorder traversal from finite trees to trees that are not necessarily finite. For trees over a well-ordered set, the Kleene–Brouwer order is itself a well-ordering if and only if the tree has no infinite branch. It is named after Stephen Cole Kleene, Luitzen Egbertus Jan Brouwer, Nikolai Luzin, and Wacław Sierpiński.
New!!: Large countable ordinal and Kleene–Brouwer order · See more »
Kripke–Platek set theory
The Kripke–Platek axioms of set theory (KP), pronounced, are a system of axiomatic set theory developed by Saul Kripke and Richard Platek.
New!!: Large countable ordinal and Kripke–Platek set theory · See more »
Kurt Schütte
Kurt Schütte (14 October 1909, Salzwedel – 18 August 1998, Munich) was a German mathematician who worked on proof theory and ordinal analysis.
New!!: Large countable ordinal and Kurt Schütte · See more »
Large cardinal
In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.
New!!: Large countable ordinal and Large cardinal · See more »
Large Veblen ordinal
In mathematics, the large Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen.
New!!: Large countable ordinal and Large Veblen ordinal · See more »
Mahlo cardinal
In mathematics, a Mahlo cardinal is a certain kind of large cardinal number.
New!!: Large countable ordinal and Mahlo cardinal · See more »
Oracle machine
In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems.
New!!: Large countable ordinal and Oracle machine · See more »
Ordinal analysis
In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength.
New!!: Large countable ordinal and Ordinal analysis · See more »
Ordinal arithmetic
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation.
New!!: Large countable ordinal and Ordinal arithmetic · See more »
Ordinal collapsing function
In mathematical logic and set theory, an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive large countable ordinals, whose principle is to give names to certain ordinals much larger than the one being defined, perhaps even large cardinals (though they can be replaced with recursively large ordinals at the cost of extra technical difficulty), and then “collapse” them down to a system of notations for the sought-after ordinal.
New!!: Large countable ordinal and Ordinal collapsing function · See more »
Ordinal notation
In mathematical logic and set theory, an ordinal notation is a partial function from the set of all finite sequences of symbols from a finite alphabet to a countable set of ordinals, and a Gödel numbering is a function from the set of well-formed formulae (a well-formed formula is a finite sequence of symbols on which the ordinal notation function is defined) of some formal language to the natural numbers.
New!!: Large countable ordinal and Ordinal notation · See more »
Ordinal number
In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.
New!!: Large countable ordinal and Ordinal number · See more »
Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
New!!: Large countable ordinal and Peano axioms · See more »
PostScript
PostScript (PS) is a page description language in the electronic publishing and desktop publishing business.
New!!: Large countable ordinal and PostScript · See more »
Proof theory
Proof theory is a major branchAccording to Wang (1981), pp.
New!!: Large countable ordinal and Proof theory · See more »
Recursive ordinal
In mathematics, specifically set theory, an ordinal \alpha is said to be recursive if there is a recursive well-ordering of a subset of the natural numbers having the order type \alpha.
New!!: Large countable ordinal and Recursive ordinal · See more »
Regular cardinal
In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality.
New!!: Large countable ordinal and Regular cardinal · See more »
Second-order arithmetic
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets.
New!!: Large countable ordinal and Second-order arithmetic · See more »
Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
New!!: Large countable ordinal and Set theory · See more »
Small Veblen ordinal
In mathematics, the small Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen.
New!!: Large countable ordinal and Small Veblen ordinal · See more »
Stephen Cole Kleene
Stephen Cole Kleene (January 5, 1909 – January 25, 1994) was an American mathematician.
New!!: Large countable ordinal and Stephen Cole Kleene · See more »
Transitive model
In mathematical set theory, a transitive model is a model of set theory that is standard and transitive.
New!!: Large countable ordinal and Transitive model · See more »
Turing machine
A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.
New!!: Large countable ordinal and Turing machine · See more »
Veblen function
In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced by Oswald Veblen in.
New!!: Large countable ordinal and Veblen function · See more »
Zermelo set theory
Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory.
New!!: Large countable ordinal and Zermelo set theory · See more »
Zermelo–Fraenkel set theory
In mathematics, 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 paradox.
New!!: Large countable ordinal and Zermelo–Fraenkel set theory · See more »
Redirects here:
Large countable ordinals, Large ordinal, Large ordinals, Mahlo ordinal.
References
[1] https://en.wikipedia.org/wiki/Large_countable_ordinal
