Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Download
Faster access than browser!
And Ads-free!

Zero sharp

In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe. [1]

34 relations: Axiom of constructibility, Baire space (set theory), Cardinal number, Cardinality, Chang's conjecture, Cofinal (mathematics), Cofinality, Constructible universe, Donald A. Martin, Erdős cardinal, Forcing (mathematics), Gödel numbering, Generic filter, Hereditarily finite set, Indiscernibles, Ineffable cardinal, Jack Silver, Jensen's covering theorem, Large cardinal, Leo Harrington, Lightface analytic game, Measurable cardinal, Ramsey cardinal, Regular cardinal, Ronald Jensen, Set theory, Springer Science+Business Media, Tarski's undefinability theorem, Transactions of the American Mathematical Society, Turing degree, Uncountable set, Well-formed formula, Zermelo–Fraenkel set theory, Zero dagger.

Axiom of constructibility

The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible.

New!!: Zero sharp and Axiom of constructibility · See more »

Baire space (set theory)

In set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology.

New!!: Zero sharp and Baire space (set theory) · See more »

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.

New!!: Zero sharp and Cardinal number · See more »

Cardinality

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

New!!: Zero sharp and Cardinality · See more »

Chang's conjecture

In model theory, a branch of mathematical logic, Chang's conjecture, attributed to Chen Chung Chang by, states that every model of type (ω2,ω1) for a countable language has an elementary submodel of type (ω1, ω).

New!!: Zero sharp and Chang's conjecture · See more »

Cofinal (mathematics)

In mathematics, let A be a set and let ≤ be a binary relation on A. Then a subset B of A is said to be cofinal if it satisfies the following condition: This definition is most commonly applied when A is a partially ordered set or directed set under the relation ≤. Cofinal subsets are very important in the theory of directed sets and nets, where “cofinal subnet” is the appropriate generalization of “subsequence”.

New!!: Zero sharp and Cofinal (mathematics) · See more »

Cofinality

In mathematics, especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of the cofinal subsets of A. This definition of cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member.

New!!: Zero sharp and Cofinality · 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!!: Zero sharp and Constructible universe · See more »

Donald A. Martin

Donald A. (Tony) Martin (born December 24, 1940) is an American set theorist and philosopher of mathematics at UCLA, where he is a member of the faculty of mathematics and philosophy.

New!!: Zero sharp and Donald A. Martin · See more »

Erdős cardinal

In mathematics, an Erdős cardinal, also called a partition cardinal is a certain kind of large cardinal number introduced by.

New!!: Zero sharp and Erdős cardinal · See more »

Forcing (mathematics)

In the mathematical discipline of set theory, forcing is a technique discovered by Paul Cohen for proving consistency and independence results.

New!!: Zero sharp and Forcing (mathematics) · See more »

Gödel numbering

In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number.

New!!: Zero sharp and Gödel numbering · See more »

Generic filter

In the mathematical field of set theory, a generic filter is a kind of object used in the theory of forcing, a technique used for many purposes, but especially to establish the independence of certain propositions from certain formal theories, such as ZFC.

New!!: Zero sharp and Generic filter · See more »

Hereditarily finite set

In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets.

New!!: Zero sharp and Hereditarily finite set · See more »

Indiscernibles

In mathematical logic, indiscernibles are objects which cannot be distinguished by any property or relation defined by a formula.

New!!: Zero sharp and Indiscernibles · See more »

Ineffable cardinal

In the mathematics of transfinite numbers, an ineffable cardinal is a certain kind of large cardinal number, introduced by.

New!!: Zero sharp and Ineffable cardinal · See more »

Jack Silver

Jack Howard Silver (born 23 April 1942) is a set theorist and logician at the University of California, Berkeley.

New!!: Zero sharp and Jack Silver · See more »

Jensen's covering theorem

In set theory, Jensen's covering theorem states that if 0# does not exist then every uncountable set of ordinals is contained in a constructible set of the same cardinality.

New!!: Zero sharp and Jensen's covering theorem · 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!!: Zero sharp and Large cardinal · See more »

Leo Harrington

Leo Anthony Harrington (born 1946) is a professor of mathematics at the University of California, Berkeley who works in recursion theory, model theory, and set theory.

New!!: Zero sharp and Leo Harrington · See more »

Lightface analytic game

In descriptive set theory, a lightface analytic game is a game whose payoff set A is a \Sigma^1_1 subset of Baire space; that is, there is a tree T on \omega\times\omega which is a computable subset of (\omega\times\omega)^.

New!!: Zero sharp and Lightface analytic game · See more »

Measurable cardinal

In mathematics, a measurable cardinal is a certain kind of large cardinal number.

New!!: Zero sharp and Measurable cardinal · See more »

Ramsey cardinal

In mathematics, a Ramsey cardinal is a certain kind of large cardinal number introduced by and named after Frank P. Ramsey.

New!!: Zero sharp and Ramsey cardinal · See more »

Regular cardinal

In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality.

New!!: Zero sharp and Regular cardinal · See more »

Ronald Jensen

Ronald Björn Jensen (born April 1, 1936) is an American mathematician active in Europe, primarily known for his work in mathematical logic and set theory.

New!!: Zero sharp and Ronald Jensen · See more »

Set theory

Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects.

New!!: Zero sharp and Set theory · See more »

Springer Science+Business Media

Springer Science+Business Media or Springer is a global publishing company that publishes books, e-books and peer-reviewed journals in science, technical and medical (STM) publishing.

New!!: Zero sharp and Springer Science+Business Media · See more »

Tarski's undefinability theorem

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics.

New!!: Zero sharp and Tarski's undefinability theorem · See more »

Transactions of the American Mathematical Society

The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.

New!!: Zero sharp and Transactions of the American Mathematical Society · See more »

Turing degree

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.

New!!: Zero sharp and Turing degree · See more »

Uncountable set

In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.

New!!: Zero sharp and Uncountable set · See more »

Well-formed formula

In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word (i.e. a finite sequence of symbols from a given alphabet) that is part of a formal language.

New!!: Zero sharp and Well-formed formula · See more »

Zermelo–Fraenkel set theory

In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets free of paradoxes such as Russell's paradox.

New!!: Zero sharp and Zermelo–Fraenkel set theory · See more »

Zero dagger

In set theory, 0† (zero dagger) is a particular subset of the natural numbers, first defined by Robert M. Solovay in unpublished work in the 1960s.

New!!: Zero sharp and Zero dagger · See more »

References

[1] https://en.wikipedia.org/wiki/Zero_sharp

OutgoingIncoming
Hey! We are on Facebook now! »