On the indestructibility aspects of identity crisis

Grigor Sargsyan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We investigate the indestructibility properties of strongly compact cardinals in universes where strong compactness suffers from identity crisis. We construct an iterative poset that can be used to establish Kimchi-Magidor theorem from (in The independence between the concepts of compactness and supercompactness, circulated manuscript), i.e., that the first n strongly compact cardinals can be the first n measurable cardinals. As an application, we show that the first n strongly compact cardinals can be the first n measurable cardinals while the strong compactness of each strongly compact cardinal is indestructible under Levy collapses (our theorem is actually more general, see Sect. 3). A further application is that the class of strong cardinals can be nonempty yet coincide with the class of strongly compact cardinals while strong compactness of any strongly compact cardinal κ is indestructible under κ-directed closed posets that force GCH at κ.

Original languageEnglish (US)
Pages (from-to)493-513
Number of pages21
JournalArchive for Mathematical Logic
Issue number6
StatePublished - Jul 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Philosophy
  • Logic


  • Identity crisis
  • Indestructibility
  • Large cardinals
  • Strongly compact cardinals
  • Supercompact cardinal


Dive into the research topics of 'On the indestructibility aspects of identity crisis'. Together they form a unique fingerprint.

Cite this