One of the first formal proof systems. This is actually understandable!
This is Ciro Santilli-2020 definition of the foundation of mathematics (and the only one he had any patience to study at all).
TODO what are its limitations? Why were other systems created?
It seems to implement Zermelo-Fraenkel set theory.
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A formal system is a structured framework designed to derive theorems from a set of axioms through formal rules of inference. It consists of several key components: 1. **Alphabet**: A finite set of symbols used to construct expressions and statements within the system. 2. **Language**: The formal expressions are defined using the symbols of the alphabet based on specific grammatical rules. This includes both syntactic rules (how symbols can be combined) and semantic rules (meaning of the expressions).