logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets. The axiom of projective determinacy, abbreviated...

uniformization. AD+ Axiom of projective determinacy Topological game Ikegami, Daisuke; de Kloet, David; Löwe, Benedikt (2012-11-01). "The axiom of real Blackwell...

if it has a projective set as its winning set (see Projective determinacy). The axiom of determinacy implies that for every subspace X of the real numbers...

of determinacy Axiom of projective determinacy Martin's axiom Axiom of constructibility Rank-into-rank Kripke–Platek axioms Diamond principle Parallel...

then projective determinacy holds; that is, every game whose winning condition is a projective set is determined. From projective determinacy it follows...

ordinal determinacy. Axiom of projective determinacy Axiom of real determinacy Suslin's problem Topological game Woodin, W. Hugh (1999). The axiom of determinacy...

Just as the axiom of projective determinacy yields a canonical theory of H ℵ 1 {\displaystyle H_{\aleph _{1}}} , he sought to find axioms that would give...

Borel determinacy are studied in descriptive set theory. They are closely related to large cardinal axioms. The axiom of projective determinacy states...

study of inner models is common in the study of determinacy and large cardinals, especially when considering axioms such as the axiom of determinacy that...

Prewellordering Projective set Property of Baire Uniformization (set theory) Universally measurable set Determinacy AD+ Axiom of determinacy Axiom of projective determinacy...

Antimicrobial Photodynamic Therapy Point-defence, a category of weapons Axiom of projective determinacy, in mathematical logic Pumpe Düse, a Volkswagen Group...

Prewellordering Projective set Property of Baire Uniformization (set theory) Universally measurable set Determinacy AD+ Axiom of determinacy Axiom of projective determinacy...

that new axioms, for example the axiom of projective determinacy, might improve ZFC, but that these axioms will not allow for dependence of the continuum...

addition of axioms such as Martin's axiom or large cardinal axioms to ZFC. Some others are decided in ZF+AD where AD is the axiom of determinacy, a strong...

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...

projective determinacy[citation needed], that is a statement in the language of second-order arithmetic is provable in Z2 with projective determinacy...

the axiom of choice.) Every free abelian group is projective. Baer's criterion: Every divisible abelian group is injective. Every set is a projective object...

N. Briefly, every set is determined by its elements." AXIOM II. Axiom of elementary sets (Axiom der Elementarmengen) "There exists a set, the null set...

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...

of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at...

abstraction Axiom of choice Axiom of comprehension Axiom of Equity Axiom of extensionality Axiom of infinity Axiom of projective determinacy Axiom of reducibility...

of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation (Aussonderungsaxiom), subset axiom, axiom of...

implies that the axiom of determinacy holds in L(R) and is believed to imply the existence of an inner model with a superstrong cardinal. List of statements...

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...

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...

the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set x {\displaystyle x} the existence of a...

epistemic status below). A large cardinal axiom is an axiom stating that there exists a cardinal (or perhaps many of them) with some specified large cardinal...

theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo. Informally, the axiom states that...

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...

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...