Add support for required schema keyword

[jdorn]

The required keyword lists the specific properties of an object that must be set. Currently, all object properties are always set, so validating against this doesn't make any sense. To add support for this keyword, we can do one or both of the following:

1. Change the meaning of required to mean not-empty. This means a blank string will fail. This will be inconsistent with the specification, but more inline with other implementations and common usage. I think this should be the default behavior and have an option to use the spec definition of required instead.
2. Add a way to remove non-required properties from objects. This will open the door to supporting other schema keywords additionalProperties, patternProperties, maxProperties, and minProperties.

A potential UI for removing properties could be something like this: