An Introduction to First-Order Logic

Publisher Summary This chapter discusses the formulas that are certain finite strings of symbols. The “first” in the phrase “first-order logic” is to distinguish this form of logic from stronger logics, such as second-order or weak second-order logic, where certain extralogical notions (set or natural number) are taken as given in advance. The chapter provides information of what can and what cannot be expressed in first-order logic. Most of the examples are taken from the wealth of notions in modern algebra with which most mathematicians have at least a nodding acquaintance. The chapter also discusses many-sorted first-order logic, ω-logic, weak second-order logic, Infinitary logic, Logic with new quantifiers, and abstract model theory.