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...

ZFC: Axiom of constructibility (V=L) (which is also not a ZFC axiom) Continuum hypothesis Diamond principle Martin's axiom (which is not a ZFC axiom) Suslin...

axiom Axiom of constructibility Rank-into-rank Kripke–Platek axioms Diamond principle Parallel postulate Birkhoff's axioms (4 axioms) Hilbert's axioms (20...

models may be quite different from the properties of L {\displaystyle L} itself. Axiom of constructibility Statements true in L Reflection principle Axiomatic...

intuition and resolve CH in one direction or another. Although the axiom of constructibility does resolve CH, it is not generally considered to be intuitively...

they are both independent of ZF. The axiom of constructibility and the generalized continuum hypothesis each imply the axiom of choice and so are strictly...

language of ZFC is already provable in ZFC (Fraenkel, Bar-Hillel & Levy 1973, p.72). Alternatively, Gödel showed that given the axiom of constructibility one...

axiom of constructibility (V = L) implies the existence of a Suslin tree. The diamond principle ◊ says that there exists a ◊-sequence, a family of sets Aα...

The axiom of extensionality, also called the axiom of extent, is an axiom used in many forms of axiomatic set theory, such as Zermelo–Fraenkel set theory...

Suslin lines exist if the diamond principle, a consequence of the axiom of constructibility V = L, is assumed. (Jensen's result was a surprise, as it had...

ISBN 3-540-00384-3. F. Rowbottom, "Some strong axioms of infinity incompatible with the axiom of constructibility". Annals of Mathematical Logic vol. 3, no. 1 (1971)...

(See the Lévy hierarchy.) Axiom of extensionality: Two sets are the same if and only if they have the same elements. Axiom of induction: φ(a) being a formula...

consistency of both of the following: The axiom of constructibility (which asserts that all sets are constructible); Martin's axiom plus the negation of the continuum...

Axiom Space, Inc., also known as Axiom Space, is an American privately funded space infrastructure developer headquartered in Houston, Texas. Founded in...

In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty...

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...

an axiom is a premise or starting point for reasoning. In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are...

an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom. An axiom schema is a formula in the metalanguage of an axiomatic...

existence of 0#, or indeed that every set with rank less than κ has a sharp. This in turn implies the falsity of the Axiom of Constructibility of Kurt Gödel...

Gödel's constructible universe L and the axiom of constructibility Inaccessible cardinals yield models of ZF and sometimes additional axioms, and are...

than the axiom of choice by using forcing to construct a model that satisfies the axiom of choice and all the axioms of NBG except the axiom of global choice...

Hamkins, Joel David (2014), "A multiverse perspective on the axiom of constructibility", Infinity and truth, Lect. Notes Ser. Inst. Math. Sci. Natl....

But some classical theories, such as ZFC plus the axiom of constructibility, do have a weaker form of the existence property (Rathjen 2005). Heyting arithmetic...

that are not sets, including a class of all sets. It replaces several of the standard ZF axioms for constructing new sets with a principle known as Ackermann's...

axiom (usually together with the negation of the continuum hypothesis), Martin's maximum ◊ and ♣ Axiom of constructibility (V=L) proper forcing axiom...

not constructible. "Axiom of power set | set theory | Britannica". www.britannica.com. Retrieved 2023-08-06. Devlin, Keith (1984). Constructibility. Berlin:...

by Kurt Gödel in his proof that the axiom of constructibility implies GCH. Devlin, Keith (1984). Constructibility. Springer. ISBN 3-540-13258-9. (theorem...

mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...

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 non-empty...

In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line...