Singular Failures of GCH and Level by Level Equivalence ∗†

نویسنده

  • Arthur W. Apter
چکیده

We construct a model for the level by level equivalence between strong compactness and supercompactness in which below the least supercompact cardinal κ, there is an unbounded set of singular cardinals which witness the only failures of GCH in the universe. In this model, the structure of the class of supercompact cardinals can be arbitrary.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Inaccessible Cardinals, Failures of GCH, and Level-by-Level Equivalence

We construct models for the level by level equivalence between strong compactness and supercompactness containing failures of GCH at inaccessible cardinals. In one of these models, no cardinal is supercompact up to an inaccessible cardinal, and for every inaccessible cardinal δ, 2δ > δ++. In another of these models, no cardinal is supercompact up to an inaccessible cardinal, and the only inacce...

متن کامل

A note on tall cardinals and level by level equivalence

Starting from a model V “ZFC + GCH + κ is supercompact + No cardinal is supercompact up to a measurable cardinal”, we force and construct a model V P such that V P “ZFC + κ is supercompact + No cardinal is supercompact up to a measurable cardinal + δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generaliz...

متن کامل

Large Cardinals and Lightface Definable Well-Orders, without the GCH

This paper deals with the question whether the assumption that for every inaccessible cardinal κ there is a well-order of H(κ+) definable over the structure 〈H(κ+),∈〉 by a formula without parameters is consistent with the existence of (large) large cardinals and failures of the GCH. We work under the assumption that the SCH holds at every singular fixed point of the i-function and construct a c...

متن کامل

Violating the Singular Cardinals Hypothesis Without

We extend a transitive model V of ZFC +GCH cardinal preservingly to a model N of ZF + “GCH holds below אω” + “there is a surjection from the power set of אω onto λ” where λ is an arbitrarily high fixed cardinal in V . The construction can roughly be described as follows: add אn+1 many Cohen subsets of אn+1 for every n < ω , and adjoin λ many subsets of אω which are unions of ω-sequences of thos...

متن کامل

L - like Combinatorial Principles and Level by Level Equivalence ∗ †

We force and construct a model in which GCH and level by level equivalence between strong compactness and supercompactness hold, along with certain additional “L-like” combinatorial principles. In particular, this model satisfies the following properties: 1. ♦δ holds for every successor and Mahlo cardinal δ. 2. There is a stationary subset S of the least supercompact cardinal κ0 such that for e...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014