register_post_type('my_custom_post', array(
            'labels'        => array(
                'name'          => __('custom name', 'my_custom_post'),
                'singular_name' => __('custom name', 'my_custom_post'),
            ),
            'public'        => true,
            'has_archive'   => true,
            'show_ui'       => true,
            'capabilities' => array(
              'edit_post'          => 'read',
              'read_post'          => 'read',
              'delete_post'        => 'read',
              'edit_posts'         => 'read',
              'edit_others_posts'  => 'manage_options',
              'publish_posts'      => 'read',
              'read_private_posts' => 'manage_options',
              'create_posts'       => 'read',
            )
        ));