On the consistency strength of the inner model hypothesis

S-D Friedman, PD Welch, WH Woodin

Research output: Contribution to journalArticle (Academic Journal)peer-review

15 Citations (Scopus)


The Inner Model Hypothesis (IMH) and the Strong Inner Model Hypothesis (SIMH) were introduced in [4]. In this article we establish some upper and lower bounds for their consistency strength. We repeat the statement of the IMH, as presented in [4]. 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 InnerModelHypothesis asserts that the universe has been maximised with respect to internal consistency:
Translated title of the contributionOn the consistency strenght of the inner model hypopethsis
Original languageEnglish
Pages (from-to)391 - 400
Number of pages10
JournalJournal of Symbolic Logic
Issue number2
Publication statusPublished - Jun 2008


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