The Largest Suslin Axiom

Grigor Sargsyan is Professor at the Institute of Mathematics of the Polish Academy of Sciences. He holds a Ph.D. in mathematics from the University of California, Berkeley. His thesis, which is the precursor of the work presented in this book, received Association of Symbolic Logic's Sacks Prize. He later received the National Science Foundation's Career Award, which was awarded to complete the work carried out in this book. Nam Trang is Assistant Professor of Mathematics at the University of North Texas. He holds a Ph.D. in mathematics from the University of California, Berkeley. He is the recipient of the National Science Foundation's two regular grants and a Career Award, part of which supports the writing of this book. He also received an Outstanding Research Award from the UNT Department of Mathematics.

• 1. Introduction; 2. Hybrid J-structures; 3. Short tree strategy mice; 4. A comparison theory of HOD mice; 5. HOD mice revisited; 6. The internal theory of LSA HOD mice; 7. Analysis of HOD; 8. Models of LSA as derived models; 9. Condensing sets; 10. Applications; 11. A proof of square in LSA-small HOD mice; 12. LSA from PFA; References; Index.