1 research outputs found
On logics extended with embedding-closed quantifiers
We study first-order as well as infinitary logics extended with quantifiers
closed upwards under embeddings. In particular, we show that if a chain of
quasi-homogeneous structures is sufficiently long then a given formula of such
a logic is eventually equivalent to a quantifier-free formula in that chain. We
use this fact to produce a number of undefinability results for logics with
embedding-closed quantifiers. In the final section we introduce an
Ehrenfeucht-Fra\"iss\'e game that characterizes the -equivalence between
structures, where is the infinitary logic extended with
all embedding-closed quantifiers. In conclusion, we provide an application of
this game illustrating its use.Comment: 29 pages, 3 figure