branch of mathematical logic, an inner model for a theory T is a substructure of a model M of a set theory that is both a model for T and contains all the ordinals...

set theory, inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof. Ordinarily these models are transitive...

continuum hypothesis or the axiom of choice, the inner model L constructed inside the original model will satisfy both the generalized continuum hypothesis...

Continuum-Hypothesis". In this paper, he proved that the constructible universe is an inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiom...

certain large cardinals leads to the existence of a canonical inner model, called the core model, that is, in a sense, maximal and approximates the structure...

{\displaystyle j:V\to M} from V {\displaystyle V} into a transitive inner model M {\displaystyle M} with critical point κ {\displaystyle \kappa } and...

there exists an elementary embedding j : V → M from V into a transitive inner model M with critical point κ and V j ( κ ) {\displaystyle V_{j(\kappa )}}...

consistency of V=L is provable by inner models but not forcing: every model of ZF can be trimmed to become a model of ZFC + V=L. The diamond principle...

smallest inner model containing the real numbers. Another consequence is the failure of square principles and hence existence of inner models with many...

from the Von Neumann universe V {\displaystyle V} into a transitive inner model M {\displaystyle M} with critical point κ {\displaystyle \kappa } and...

follows. Assuming the existence of an inaccessible cardinal, there is an inner model of ZF + DC of a suitable forcing extension V[G] such that every set of...

In mathematical set theory, Chang's model is the smallest inner model of set theory closed under countable sequences. It was introduced by Chang (1971)...

domain of M is a proper class, then M is a class model. An inner model is necessarily a class model. Cohen, P. J. (1966). Set theory and the continuum...

proposed, in 2018, a three-layer model, with an "inner inner core" (IIC) with about 500 km radius, an "outer inner core" (OIC) layer about 600 km thick...

constructible universe L {\displaystyle L} is the core model—that is, the canonical inner model that approximates the large cardinal structure of the universe...

cardinal properties). Generalizations of this axiom are explored in inner model theory. The axiom of constructibility implies the axiom of choice (AC)...

set theory, the core model is a definable inner model of the universe of all sets. Even though set theorists refer to "the core model", it is not a uniquely...

vehicle. Instead, it represents them as specific to a Car. We can model this notion using inner classes as follows: We have the top-level class Car. Instances...

University. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinals, the Woodin cardinals, bears...

constructible universe L, an inner model of ZF set theory, assuming only the axioms of ZF. The existence of an inner model of ZF in which additional axioms...

theory Black flight and white flight Concentric zone model Ghetto Industrial deconcentration Inner-City Games Skid row Slum Suburban colonization Urban...

{\displaystyle j} from the universe V {\displaystyle V} into a transitive inner model M {\displaystyle M} with critical point κ {\displaystyle \kappa } , j...

supercompact cardinal. However, a proof is unlikely until a canonical inner model theory for supercompact cardinals is developed. Jech obtained a variant...

Intrapersonal communication (also known as autocommunication or inner speech) is communication with oneself or self-to-self communication. Examples are...

October 6, 2019. "James Denton, the Desperate Housewives star channels his inner model". First Luxe. Archived from the original on April 18, 2012. Retrieved...

The inner team is a personality model created by German psychologist Friedemann Schulz von Thun. The plurality of the human inner life or facets of the...

The concentric zone model, also known as the Burgess model or the CCD model, is one of the earliest theoretical models to explain urban social structures...

that of subtle cardinals and remarkable cardinals inner model An inner model is a transitive model of ZF containing all ordinals Int Interior of a subset...

greatly Mahlo, etc. are preserved if we replace the universe by an inner model. Every reflecting cardinal has strictly more consistency strength than...

exists an elementary embedding j from the universe V into a transitive inner model M with critical point κ and V λ ⊆ M {\displaystyle V_{\lambda }\subseteq...