"that actually exist" is grammatically correct and can be used in written English.
It is used to refer to things or ideas that are real and present in the world. Example: The rumors about a secret underground city in Chicago are just that - rumors. There is no evidence to suggest that such a place actually exists.
Here is another A-theoretic view: when t is the unique objective present, all temporal perspectives that actually exist include t, truths indexed to t are true at all actually existing perspectives, but there is no such thing as truth simpliciter.
Various combinations of programs are possible, and it is difficult to summarize all the arrangements that actually exist.
They recently reorganized their categories in an attempt to better represent the types of recordings that actually exist in the world.
And why deal with threats that actually exist when you can spend your time obsessing over things Russia might do down the road?
Calculations of inspection fees for weight scales and gasoline pumps were made using numbers for scales and pumps far beyond the numbers that actually exist in the county.
In the same way, writing about situations that actually exist aid the reader's journey to becoming more accepting of those different from themselves.
(Seriously, that is an actual thing that actually exists).
Then, at \ \Gamma, \exists^{E}x\Box P x)\) says something that actually exists has, in all alternative states, the property of existing in the state \ \Gamma\).
The correspondence of our thoughts to reality, that is the truth of our ideas, depends on something that actually exists and not on something independent of existence.
Consider all of the following devices (that actually existed).
Is all this really necessary to fight the terrorist threat that actually exists?
