and transitive means that the model is a transitive set or class. An inner model is a transitive model containing all ordinals. A countable transitive model...

absolute for transitive classes. A transitive set (or class) that is a model of a formal system of set theory is called a transitive model of the system...

standard model M that satisfies the additional transitivity condition that x ∈ y ∈ M implies x ∈ M is a standard transitive model (or simply a transitive model)...

(well-founded, extensional) model is isomorphic to a transitive one. (If the model M is not transitive things get messier, as M′s interpretation of what...

Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M...

Stochastic transitivity models are stochastic versions of the transitivity property of binary relations studied in mathematics. Several models of stochastic...

before selecting a model of set theory. Another difference is that the statement "For every transitive model of ZFC there is a larger model of ZFC in which...

mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For finite...

is isomorphic to a transitive model of ZF and such a transitive model is unique. Saying that the membership relation of some model of ZF is well-founded...

standard transitive model can be obtained from any standard model through the Mostowski collapse lemma, but the existence of any standard model of Z F C...

model of T the domain of N is a transitive class of M N contains all ordinals in M then we say that N is an inner model of T (in M). Usually T will equal...

In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates...

Berkeley cardinal is a cardinal κ in a model of Zermelo–Fraenkel set theory with the property that for every transitive set M that includes κ and α < κ, there...

called transitive if for any two points x, y ∈ X there exists a g ∈ G so that g ⋅ x = y. The action is simply transitive (or sharply transitive, or regular)...

A transitive verb is a verb that entails one or more transitive objects, for example, 'enjoys' in Amadeus enjoys music. This contrasts with intransitive...

universe or in any absolute (model independent) sense. Suppose the set M is a transitive model of ZFC set theory. The transitivity of M implies that the integers...

transitive dependency is an indirect dependency relationship between software components. This kind of dependency is held by virtue of a transitive relation...

polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure...

begin with a fixed model of set theory and only consider other transitive models containing the same ordinals as the fixed model. Certain properties...

usually proved by forcing, whereby it is shown that every countable transitive model of ZFC (sometimes augmented with large cardinal axioms) can be expanded...

\alpha } -Erdős, then it is α {\displaystyle \alpha } -Erdős in every transitive model satisfying " α {\displaystyle \alpha } is countable." For a limit ordinal...

{\displaystyle F\cap E\neq \varnothing ,\,} for all E ∈ D. Similarly, if M is a transitive model of ZFC (or some sufficient fragment thereof), with P an element of...

that the membership relation is transitive on it. 4.  A transitive model is a model of set theory that is transitive and has the usual membership relation...

for formulas in Vκ in the infinitary logic L∞,ω. The least κ with a transitive model M⊂Vκ+1 extending Vκ satisfying Morse–Kelley set theory. (not a worldly...

says that for any finite set of axioms of ZFC we can find a countable transitive model satisfying these axioms. (In particular this proves that, unless inconsistent...

deterministically transitive in order to apply probabilistic models. However, transitivity will generally hold for a large number of comparisons if models such as...

that for every countable transitive model of the theory, and every forcing notion in the model, the generic extension of the model (as calculated in V) contains...

entity–relationship model (or ER model) describes interrelated things of interest in a specific domain of knowledge. A basic ER model is composed of entity...

relatively general evolutionary model. The general nature of this basic non-transitive model is widely applied in theoretical biology to explore bacterial ecology...

also contains a longer directed path from u to v. Like the transitive closure, the transitive reduction is uniquely defined for DAGs. In contrast, for a...