Inner Model Operators and the Continuum Hypothesis

Internal Consistency and the Inner Model Hypothesis

Assume that the universe V of all sets is rich in the sense that it contains inner models with large cardinals. Then what is the relationship between Easton’s model L[G] and V ? In particular, are these models compatible, in the sense that they are inner models of a common third model? If not, then the failure of GCH at every regular cardinal is consistent only in a weak sense, as it can only h...

Foundational implications of the Inner Model Hypothesis

The Inner Model Hypothesis (IMH) is a new axiomatic approach in set theory formulated by Sy-D. Friedman. The purpose of this paper is to illustrate the hypothesis, and discuss it with respect to the current debate on the consequences of independence results in set theory. © 2012 Elsevier B.V. All rights reserved.

The Continuum Hypothesis

The continuum hypotheses (CH) is one of the most central open problems in set theory, one that is important for both mathematical and philosophical reasons. The problem actually arose with the birth of set theory; indeed, in many respects it stimulated the birth of set theory. In 1874 Cantor had shown that there is a one-to-one correspondence between the natural numbers and the algebraic number...

Inner Model Operators in L(R)

On the consistency strength of the inner model hypothesis

We repeat the statement of the IMH, as presented in [5]. A sentence in the language of set theory is internally consistent iff it holds in some (not necessarily proper) inner model. The meaning of internal consistency depends on what inner models exist: If we enlarge the universe, it is possible that more statements become internally consistent. The Inner Model Hypothesis asserts that the unive...