Denumerably many isomorphism types
-
31-10-2019 - |
Question
Computability and Logic by Boolos and Burgess says that formula $\Gamma_d$ in example 12.12
∀x∀y(∃u(u ≠ x ∧ u ≡ x) ∧ ∃v(v ≠ y ∧ v ≡ y)) → x ≡ y)
supports models, whose domain is partitioned into equivalence classes of any size, e.g.
is possible. Yet, I do not understand how this is possible. Suppose my x is the first dot. Then, I can find u, which is the second dot. Similarly, let y be the first dot in the second equivalence class and another dot v is in its companion in the eqivalence class. The formula says that x and y must be in the same equivalence class. But they are obviously not!
Are they trying to cheat me?
No correct solution
Licensed under: CC-BY-SA with attribution
Not affiliated with cs.stackexchange