On Sets and Graphs

Dr. Eugenio G. Omodeo is a professor in the Department of Mathematics and Geosciences at the University of Trieste, Italy. His other publications include the Springer title Computational Logic and Set Theory. Dr. Alberto Policriti is a Professor of Computer Science in the Department of Mathematics, Computer Science, and Physics at the University of Udine, Italy. Together with Dr. Eugenio G. Omodeo, he is co-author of the Springer title Set Theory for Computing. Dr. Alexandru I. Tomescu is a postdoctoral researcher in the Department of Computer Science at the University of Helsinki, Finland.

Introduction.- Part I: Basics.- Membership and Edge Relations.- Sets, Graphs, and Set Universes.- Part II: Graphs as Sets.- The Undirected Structure Underlying Sets.- Graphs as Transitive Sets.- Part III: Sets as Graphs.- Counting and Encoding Sets.- Random Generation of Sets.- Infinite Sets and Finite Combinatorics.- Appendix: Excerpts from a Referee-Checked Proof-Script.