DEFINITION. LZF(U) is the language of ZF expanded by a unary predicate U. ZF(U) is the ZF set theory plus all the instances of the replacement schema for.
N e M is said to be an inner model of M if N is a transitive class in M containing all the ordinals and satisfying the axioms of. ZF-set theory. DEFINITION.
Then a new inner model H exists and has the following properties: (1) H ≠ HOD; (2) Th(H) = Th(HOD); (3) there is j: H → H; (4) there is a c.u.b. ...
Apr 28, 2021 · I will now attempt to build a model of ZFCP out of the pieces of the inner model of ZFC. On a high level, I will use 1, 2, and 3 as type tags.
Inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof. Ordinarily these models are transitive subsets or ...
Mar 26, 2021 · There is no inner model or forcing-like construction that will give you a model, since the collection of natural numbers needs to grow.
Bibliographic details on A New Inner Model for ZFC.
Nov 1, 2024 · Abstract:An elementary embedding j:M\rightarrow N between two inner models of ZFC is cardinal preserving if M and N correctly compute the class ...
2. ZFC does not decide whether all projective sets of reals are Lebesgue measurable. 3. ZFC does not decide the Continuum Hypothesis.
The goal of this survey paper is to give an overview of recent developments in inner model theory. We discuss several most important questions in the field ...