Descriptive set theory

Descriptive set theory is like playing with blocks, but instead of blocks, we use sets of numbers or other objects. We call these sets "descriptive" because they describe certain properties or characteristics that the objects in them have. It's like putting all the yellow blocks together in one pile, or all the blocks that make a specific shape in another pile.

In descriptive set theory, we start with some basic sets and rules to build more complicated ones. We call these basic sets "Borel sets" and they're like the building blocks of our set world. We can combine Borel sets in different ways to build more complicated sets, like adding two piles of blocks together or stacking them in a specific order.

But we don't stop there! We can also use functions and operations on these sets to build even more sets. Just like you might use blocks to build a tower or a fort, we can use sets to build things like mathematical functions or infinite sequences of numbers.

And just like with blocks, we can ask questions about our sets. For example, we might wonder if a certain object is in a particular set, or if two sets are equal to each other. These questions can be tricky to answer in descriptive set theory, because some sets are very complicated and don't have straightforward answers.

In the end, descriptive set theory is a way of organizing and studying sets of numbers or other objects. It's like building a world out of blocks, where we can combine them in creative ways and discover new things about them.