# How is uncountability characterized in second order logic?

1. Jun 10, 2012

### mpitluk

How is uncountability characterized in second order logic?

2. Jun 20, 2012

### lugita15

A set is infinite if it can be put in one-to-one correspondence with one of its proper subsets. A set is countably infinite if it is infinite and it can be put in one-to-one correspondence with every one of its infinite subsets. A set is uncountably infinite if it is infinite but not countably infinite.