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;
2014-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1109740
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