Thursday, November 12, 16:00-17:30, East Hall 3096
Around 2005, Greg Hjorth proved that if there exists a counterexample to Vaught’s Conjecture, then there exists one with no model in “aleph_2”. The proof uses Descriptive Set Theory. This result was later improved by John Baldwin, Sy Friedman, Martin Koerwien, and Chris Laskowski:
Theorem. If there exists a counterexample to Vaught’s Conjecture, then there
exists one with only maximal models in “aleph_1”.
Hjorth’s proof uses Descriptive Set Theory, while the second proof uses Model Theory. During the talk we will present the machinery behind the second result (absolute indiscernibles plus characterizing cardinals) and survey related results.