Write SQL query to solve given problem: How many 4-year public institutions are there in the state of Florida? Give all of their names.. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT T1.chronname FROM institution_details AS T1 INNER JOIN state_sector_details AS T2 WHERE T2.level = '4-year' AND T2.control = 'Public' AND T2.state = 'Florida'