@mbwkam, Yes, they are a "real" vintage set almost certainly designed by Maurice Burke for Arkana (UK) in the style of Saarinen. Look up images of Burke "tulip" and "propeller" chairs for comparison. Screw holes around the top edge of the table base is a dead giveaway that it's not by Knoll.
This set of chairs still looks of good quality. Even though it's white, it doesn't look too old.
On a tangent, a friend e-mailed me a single photo earlier this week asking if I knew what it was. At a glance, I was able to quickly advise that it was an Eames La Fonda chair, designed for a Mexican restaurant in the base of the Time and Life Building in NYC. As nice a design as it is, especially the "La Fonda" base, it is only the third best piece that the Eames' designed for that building, behind the three walnut stools and the Executive Chair.
Anyway, I made the quick ID without close examination. After being sent additional photos of the backside, underside, and base closeup, I realized that it was not a legit Herman Miller-made La Fonda, but a "heavily inspired" design by Burke. I was not previously aware that Burke had done a La Fonda design.
@cdsilva, I have not seen any of those in person before, yet your description sounded so familiar somehow!
http://designaddict.com/community/identification/eames-or-not-la-fonda-ish-fibreglass-chair/
For those interested in more info about the La Fonda chairs (both arm and side), this website is a good resource: https://eames.com/en/lafonda-arms
Fun fact: the Mad Man offices were set in the Time and Life Building for a few seasons, and they even used Executive Chairs in their conference rooms.
@cdsilva, You'll notice that the chairs in that still from "Mad Men" have "5-star" bases! Oops!
Also on TV, modified Burke chairs were used on the set of the Original "Star Trek" series.
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