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...

Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by choosing...

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...

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...

to  f . Thus, the existence of an ω 1 {\displaystyle \omega _{1}} -Erdős cardinal implies that the axiom of constructibility is false. The least ω {\displaystyle...

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...

of logic, mathematics, and computer science that use it, the axiom of extensionality, axiom of extension, or axiom of extent, is one of the axioms of...

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...

(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...

The existence of a Ramsey cardinal implies the existence of 0# and this in turn implies the falsity of the Axiom of Constructibility of Kurt Gödel. A...

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...

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

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

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...

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...

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

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...

was the constructible universe L developed by Kurt Gödel. Every model M of ZF has an inner model LM satisfying the axiom of constructibility, and this...

neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted Zermelo–Fraenkel set theory, assuming that its axioms are consistent...

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...

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:...

generally has poor constructibility or decidability properties). Duck typing Identity of indiscernibles Structural typing Univalence axiom Intensional Logic...

model of ZF, then the smallest such set is such a Lκ. This set is called the minimal model of ZFC, and also satisfies the axiom of constructibility V=L...