You could add table like "post_access" with two columns post_id and user_id.
There are some possible tricks to prevent fast growing of this table:
- Author of the post could see it without adding of record to post_access
- Post table could have flag field "ispublic", and this post is visible to every one
- You could create user groups (additional table) and use post access not for users, but for groups (this make sense if you expect some grouping of users)