If \(\varphi\) is a scattered sentence of \(L_\) (i.e., one with at least one model but no perfect set of countable models) then associated to \(\varphi\) is its Morley tree. Each node of this tree is a countable theory which is atomic for a countable fragment of \(L_\) containing \(\varphi\). The Morley tree has height at most \(\omega_1\) and Vaught's conjecture asserts that its height is in fact less than \(\omega_1\). Using a generic version of the Morley tree together with a notion of fragment embedding, I'll prove a theorem of Harrington which states that if \(\varphi\) is a counterexample to Vaught's conjecture then there are models of \(\varphi\) with Scott rank arbitrarily large below \(\omega_2\).
Vaught's Conjecture, the Generic Morley Tree and Fragment Embeddings
07.03.2013 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25