The modern state of Indonesia was established on 17th August 1945, 10:00am, Jakarta, when the independence of Indonesia was declared after Japan surrended. Time source: star4cast.com.
The international recognition of Indonesia's independence didn't came until 27th December 1949, when the Netherlands gave up attemtping to reoccupy their former East Indies colonies.
Major events in the modern history of Indonesia:
A very detailed timeline of Indonesia's history is available here.
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