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...

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...

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...

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...

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...

from the Von Neumann universe 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 )}}...

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)...

{\displaystyle j:V\to M} from 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...

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...

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

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

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

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...

universe L {\displaystyle 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...

In set theory, L(R) (pronounced L of R) is the smallest transitive inner model of ZF containing all the ordinals and all the reals. L(R) can be constructed...

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

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

The minimal model of set theory has no inner models other than itself. In particular it is not possible to use the method of inner models to prove that...

philosophy, Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an uncountable set. The paradox...

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...

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

A large language model (LLM) is a language model trained with self-supervised machine learning on a vast amount of text, designed for natural language...

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...

H_{\aleph _{1}}\subset L(R)} , where L(R) is the smallest transitive inner model of ZF containing all the ordinals and all the reals. Codes are useful...

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...

inconsistent with the axiom of choice. It also implies the existence of inner models with certain large cardinals. ADR is equivalent to AD plus the axiom...