Formal system

Books that work as introduction to mathematics, either begin by introducing sets since set theory, namely ZFC, is currently considered as the foundational theory of math (from which all of mathematics can be derived), or they first touch on a formal (propositional) logic system since it's the simplest formal system.

On the one hand sets need fomal logic as they utilize logical symbols as soon as the set notation is introduced. By the way, the view that logic comes before math, i.e. that math is part of logic is called logicism.

propositional -> predicate -> higer-order logic systems -> ... ↓ ↓ set set set set set -> relations -> orders -> functions -> ...

lamda calculus || SK combinatorics || PRF