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In , Shelah and Stanley constructed a κ +-Aronszjan tree with an ascent path using κ. We show that κ,2 does not imply the existence of Aronszajn trees with ascent paths. The proof goes through an intermediate combinatorial principle, which we investigate further.
These are the notes for my quarter-long course on basic stability theory at UCLA (MATH 285D, Winter 2015). The presentation highlights some relations to set theory and cardinal arithmetic, reflecting my impression about the tastes of the audience. We develop the general theory of local stability instead of specializing to the finite rank case, and touch on… (More)
Acknowledgments I would like to express my gratitude to Menachem Magidor, for his unlimited patience and inspiration, along with dedicated guidance. His willingness to present each subject in the simplest, yet most insightful manner, was instrumental for me throughout my first steps in set theory. Above any mathematical concept or proof that he explained to… (More)