What Is Mathematical Logic?

Guillermo Badia is Senior Lecturer at the University of Queensland, Australia, where he teaches mathematical logic and is on the editorial board of the Springer journal Archive for Mathematical Logic. He has published over 40 papers on formal logic. From 2022 to 2025 his research is supported by a Discovery Early Career Researcher Award of the Australian Research Council.John N. Crossley is Emeritus Professor at Monash University, Australia, where he was Professor of Pure Mathematics and of Logic. He has published extensively on logic, theoretical computer science, history of mathematics, and medieval and Asian history.John C. Stillwell is Emeritus Professor of the University of San Francisco and former Associate Professor at Monash University, Australia. He has been given many awards for his expository writing, including 16 books, on mathematics. He has published extensively on mathematics and logic, particularly from the historical viewpoint.

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• 1: Historical survey 2: The completeness of first-order logic 3: Model theory 4: Turing machines 5: Gödel's incompleteness theorems 6: Computability in practice 7: Set theory 8: Beyond first-order logic 9: Further topics