Spahn continuum hypothesis (Rev #3)

For context see the topos Set?.

Definition

The continuum hypothesis asserts that there is no strict inequality of cardinal numbers?

|\mathbb{N}|\lt \alpha\lt |\Omega^\mathbb{N}|

where the leftest symbol dnotes the cardinality of the natural-numbers object? $\mathbb{N}$ in Set? and the rightest symbol denotes its power object?.

Theorem

There exists a boolean topos in which the axiom of choice holds and the continuum hypothesis fails.

Definition

(Cohen topos?)

References

André Joyal, Ieke Moerdijk, sheaves in geometry and logic, VI.2, VI.3
M.C. Fitting, “Intuitionistic logic, model theory and forcing” , North-Holland (1969)

Revision on June 19, 2012 at 14:24:38 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.