#foundations
03. Logic and Foundations
This volume develops formal logic, set theory, computability, and the foundations of mathematics in a unified way, where syntax, semantics, proof, and computation are treated as precise mathematical objects. Part I. Propositional and First-Order Logic Chapter 1. Propositional Logic This chapter introduces the basic language of propositional logic, its semantics, equivalence laws, normal forms, and the relation between proof and truth. 1.1 Syntax: Variables, Connectives 1.2 Semantics: Truth Tables 1.3...
00. General Mathematics
This volume establishes the meta-layer of mathematics. It covers language, structure, methodology, and cross-cutting tools that apply across all branches. The scope follows MSC 00: classification, exposition, philosophy, and general methods. Part I. What Mathematics Is Chapter 1. Nature of Mathematical Objects 1.1 Abstract objects and structures 1.2 Sets, types, and universes 1.3 Equality, identity, and equivalence 1.4 Finite vs infinite objects 1.5 Constructive vs classical viewpoints Chapter 2. Mathematical...