The gch tag has no wiki summary.

**3**

votes

**1**answer

175 views

### Failure of GCH at indescribable cardinals

Can $\Pi^m_n$ indescribable cardinal be the first one where $\text{GCH}$ fails?
Hauser showed in
Hauser,K.: Indescribable cardinals and elementary embeddings.
J. Symb. Logic 56, 439457 (1991)
that ...

**5**

votes

**4**answers

335 views

### do behavior of gimel or GCH determine all infinte products of cardinals?

Let $Card$ be the class of infinite cardinals and $p\colon Card^2\to Card$ be given by $(\kappa,\lambda)\mapsto\kappa^\lambda$.
Assuming GCH it is known that $p(\kappa,\lambda)$ is either $\kappa$ (if ...

**3**

votes

**1**answer

218 views

### The canonical forcing of the GCH and direct limits.

The motivation for this question is that I am working through an exercise to force the GCH (generalized continuum hypothesis) over a model of ZFC and obtain a model of ZFC where GCH holds.
The ...

**7**

votes

**4**answers

1k views

### Failure of the GCH

What is the (currently known) consistency strength of global failure of the GCH?
I do not have access to the exact statement of the original Foreman-Woodin result. My searches seem to indicate that ...