I'd look at some sort of nested UI i.e. a UITableView that has just A, B, C etc to start with and when the user presses on a row show another table view with all the results starting with A.
There would need to be a query that got the number of results that started with A, B, C etc so you only showed letters in the first table that actually has results but then each query in the second table would be very simple - all results starting with 'A' etc.
You'd never have to load all 20,000 results into memory at the same time :)
However, you should probably make sure that you have an index on the field that you're querying, otherwise your queries are all going to be rather slow :(
The other solution is to use a search box at the top of a table view - the user types in letters and each time the list is reduced to only results starting with that letter. That's a pretty simple query to implement :)
However, you would then still have the problem of what to do if the user hasnt typed anything in - do you show a message asking them to type or do you show all 20,000 results in an enormous list?