Answer:

In the context of mathematics and formal logic, topics like theorems and axioms fall under the domain of mathematical logic and set theory. Here's a brief explanation:

1. Theorems:

Theorems are statements in mathematics that have been proven to be true based on established axioms and previously proven theorems. The process of proving a theorem involves using logical deductions and reasoning from axioms and previously proven statements. Theorems are fundamental building blocks in mathematics and provide a foundation for further mathematical discoveries.

2. Axioms:

Axioms (or postulates) are fundamental statements or principles that are accepted without proof within a particular system of mathematics. They serve as the starting point for logical reasoning and mathematical development within that system. Axioms are assumed to be self-evident truths or statements that are so fundamental that they do not require proof.

3. Theories:

In a broader sense, theories in mathematics refer to organized sets of principles, definitions, axioms, theorems, and other related concepts that form a structured framework to understand and explain a particular branch of mathematics. For example, set theory, number theory, and graph theory are examples of mathematical theories. These theories help organize and study specific mathematical concepts in a systematic and coherent manner.

It's important to note that the specific theorems, axioms, and theories can vary based on the branch of mathematics being studied. If you're referring to a specific area of mathematics, feel free to ask for more detailed information!