the University of Michigan.
Jean Larson is Emeritus Professor of Mathematics at the University of Florida, specializing in combinatorial set theory. She received her Ph.D. in mathematics from Dartmouth University in 1972 and was E.R. Hedrick Assistant Professor at UCLA from 1972 to 1974, before joining the University of Florida in 1974.
Christopher Porter is Assistant Professor of Mathematics at Drake University, specializing in computability theory, algorithmic randomness, and the philosophy of mathematics. He received his Ph.D. in mathematics and philosophy from the University of Notre Dame in 2012, was an NSF international postdoctoral fellow at Université Paris 7 from 2012 to 2014, and a postdoctoral associate at the University of Florida from 2014 to 2016, before joining Drake University in 2016.
Jindrich Zapletal is Professor of Mathematics at University of Florida, specializing in mathematical logic and set theory. He received his Ph.D. in 1995 from the Pennsylvania State University, and held postdoctoral positions at MSRI Berkeley, Cal Tech, and Dartmouth College, before joining the University of Florida in 2000.
Contents
3. Zermelo–Fraenkel Set Theory
3.1 Historical Context
3.2 The Language of the Theory
3.5 Axiom Schema of Comprehension
3.7 Axiom Schema of Replacement
4. Natural Numbers and Countable Sets
4.1 Von Neumann’s Natural Numbers
4.3 Inductive and Recursive Definability
4.5 Countable and Uncountable Sets
5. Ordinal Numbers and the Transfinite
5.2 Transfinite Induction and Recursion
5.4 Ordinals and Well-Orderings
6. Cardinality and the Axiom of Choice
6.1 Equivalent Versions of the Axiom of Choice
6.2 Applications of the Axiom of Choice
7.1 Integers and Rational Numbers
7.4 Countable and Uncountable Sets of Reals
8.1 The Hereditarily Finite Sets
