Dacron line is used both as high strength fishing line and as kite string. Check out sporting goods/fishing supply stores, kite shops, and the internet. Here's an interesting site:

http://www.kitebuilder.com/inventory/solidcore.htm

Dacron is not the only synthetic that fits the profile, but it has been around a while longer than most of the rest.
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The ultimate result of shielding men from the effects of folly is to fill the world with fools.
-- Herbert Spencer, English Philosopher (1820-1903)