In this paper we are concerned about the ways GCH can fail in relation to rank-into-rank hypotheses, i.e., very large cardinals usually denoted by I3, I2, I1 and I0. The main results are a satisfactory analysis of the way the power function can vary on regular cardinals in the presence of rank-into-rank hypotheses and the consistency under I0 of the existence of j:Vλ+1≺Vλ+1 with the failure of GCH at λ.

Rank-into-rank hypotheses and the failure of GCH

DIMONTE, Vincenzo;
2014

Abstract

In this paper we are concerned about the ways GCH can fail in relation to rank-into-rank hypotheses, i.e., very large cardinals usually denoted by I3, I2, I1 and I0. The main results are a satisfactory analysis of the way the power function can vary on regular cardinals in the presence of rank-into-rank hypotheses and the consistency under I0 of the existence of j:Vλ+1≺Vλ+1 with the failure of GCH at λ.
File in questo prodotto:
File Dimensione Formato  
Dimonte Friedman - rankintorank and negation GCH at singular (last revision).pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 373.39 kB
Formato Adobe PDF
373.39 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/1109740
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 12
social impact