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Posted: Wednesday, December 8, 2021

Daniel Cunningham, Professor Emeritus, Mathematics, Mathematics

Daniel Cunningham, professor emeritus of mathematics, has signed a contract with De Gruyter to publish his latest book, Mathematical Logic: An Introduction. The first chapter reviews the foundational topics that are typically covered in a sophomore introduction to proof course. Chapter 2 studies the language of propositional logic. Chapter 3 investigates the more powerful language of first order logic and the notion of a formal deduction in first order logic. We prove Gödel's Completeness Theorem, a fundamental result, which asserts that a first-order sentence is valid if and only if it is deducible. Chapter 4 establishes Gödel's Incompleteness Theorem and investigates the computability concept. Mathematical logic plays a fundamental role in computer science. One of the key areas of logic that are particularly significant to computer science is computability theory. 

De Gruyter publishes first-class scholarship and has done so for more than 270 years. An international, independent publisher headquartered in Berlin—and with further offices in Boston, Beijing, Basel, Vienna, Warsaw, and Munich—it publishes over 1,300 new book titles each year and more than 900 journals in the humanities, social sciences, medicine, mathematics, engineering, computer sciences, natural sciences, and law.

Modern mathematical logic has its origins in the dream of Leibniz (the inventor of calculus) for a universal symbolic calculus that could encompass all mental activity of a logically rigorous nature, in particular, all of mathematics. This vision was too grandiose for Leibniz to realize. His writings on the subject were largely forgotten and had little influence on the actual course of events. It took Boole, Frege, Peano, Russell and Whitehead, Hilbert, Skolem, Gödel, Tarski, and their followers, armed with more powerful abstract methods, to realize a significant part of Leibniz's dream.