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The collection of countable transitive models of ZFC (in some universe) is called the hyperverse and is very similar to the "multiverse". A typical difference between the universe and multiverse views is the attitude to the continuum hypothesis. In the universe view the continuum hypothesis is a meaningful question that is either true or false ...
The axiom of global choice states that there is a global choice function τ, meaning a function such that for every non-empty set z, τ(z) is an element of z.. The axiom of global choice cannot be stated directly in the language of Zermelo–Fraenkel set theory (ZF) with the axiom of choice (AC), known as ZFC, as the choice function τ is a proper class and in ZFC one cannot quantify over classes.
Nevertheless, it is deemed unlikely that ZFC harbors an unsuspected contradiction; it is widely believed that if ZFC were inconsistent, that fact would have been uncovered by now. This much is certain — ZFC is immune to the classic paradoxes of naive set theory: Russell's paradox, the Burali-Forti paradox, and Cantor's paradox.
Here, is the set of integers, and is the set of non-negative integers. Here, all letters represent integers. We say that a map : is piecewise linear if can be defined by various affine functions with integer coefficients on each of finitely many pieces, where each piece is defined by a finite set of linear inequalities with integer coefficients.
Axiom schema of replacement: the image [] of the domain set under the definable class function is itself a set, .. Suppose is a definable binary relation (which may be a proper class) such that for every set there is a unique set such that (,) holds.
A necessary condition for a property of cardinal numbers to be a large cardinal property is that the existence of such a cardinal is not known to be inconsistent with ZF and that such a cardinal Κ would be an uncountable initial ordinal for which L Κ is a model of ZFC. If ZFC is consistent, then ZFC does not imply that any such large ...
The New 52 and Convergence restored the Pre-Crisis Multiverse; all Pre-Crisis Earths below 52 are spelled out (i.e., Earth-Three), realities from the 52 Multiverse and the New 52 Multiverse use a hyphen (Earth-3), and they later use a space (i.e., Earth 3) after the Dark Multiverse was introduced, which uses negative numbers (i.e., Earth -3).
Map of the New 52 Multiverse. In most of the DC Comics media, the Multiverse is a "cosmic construct" that is composed of the many fictional universes the stories of DC media take place in. The worlds within the multiverse share a space and fate in common, and its structure has changed several times in the history of DC Comics. [1]