Eventually different functions and inaccessible cardinals

Eventually Different Functions and Inaccessible Cardinals

Basic Facts about Inaccessible and Measurable Cardinals

Let X be an infinite set. One can check that X is infinite. The scheme ElemProp deals with a non empty set A , a set B, and a unary predicate P , and states that: P [B] provided the parameters meet the following requirement: • B ∈ {y;y ranges over elements of A : P [y]}. For simplicity, we use the following convention: N is a cardinal number, M is an aleph, X is a non empty set, Y , Z, Z1, Z2, ...

On Some Problems Involving Inaccessible Cardinals

Introduction(') Many problems in set theory and related domains are known which have the following features in common . Each of them can be formulated as the problem of determining all the infinite cardinals which have a given property P. It is known that the property P applies to all infinite cardinals which are not (strongly) inaccessible while it does not apply to the smallest inaccessible c...

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...

All Uncountable Regular Cardinals Can Be Inaccessible in Hod

Assuming the existence of a supercompact cardinal and an inaccessible above it, we construct a model of ZFC, in which all uncountable regular cardinals are inacces-