Chevalley's theorem on constructible sets

Chevalley's theorem on constructible sets means that you can make shapes called "constructible sets" by using only a few basic shapes and some special rules. It's kind of like using building blocks to make different creations!

So, what are constructible sets? They are shapes that can be made by starting with some basic shapes (like points and lines) and then using operations called "intersection" and "projection" to put more shapes together.

For example, you could start with a point (which is just a tiny dot) and then draw a line through that point. Then you could use projection to create a new point on that line. From there, you could keep adding more lines and points using these operations.

But why is this important? Chevalley's theorem says that you can make lots of different shapes this way, but you can't make every shape using only these operations. So, it helps mathematicians understand what shapes are "constructible" and what shapes aren't.

Overall, Chevalley's theorem on constructible sets is all about using simple building blocks and rules to create complex shapes, and understanding the limits of what shapes can be made in this way.