indiscernible sequence?
Morley sequence?
Ramsey theorem?
Erdos-Rado theorem?
Ehrenfeucht-Fraïssé games (back-and-forth games)
Hrushovski construction?
generic predicate?
Deductive completeness is maximality condition on a logical theory $\mathbb{T}$ saying that the deductive closure of $\mathbb{T}$ is as large as possible within the bounds of consistency.
Let $\mathbb{T}$ be a consistent logical theory over signature $\Sigma$. $\mathbb{T}$ is called complete if for any sentence $\sigma$ over $\Sigma$ either $\mathbb{T}\vdash \sigma$ or $\mathbb{T}\cup\sigma$ is inconsistent.
A geometric theory $\mathbb{T}$ over a signature $\Sigma$ is called complete if for any geometric sentence $\sigma$ over $\Sigma$ is either $\mathbb{T}$-provably equivalent to $\top$ or to $\bot$, but not both.
A geometric theory $\mathbb{T}$ is complete iff the classifying topos of $\mathbb{T}$ is two-valued.
This occurs as remark 2.5 in Caramello (2012).
Remark: a first-order theory $\mathbb{T}$ is complete in the sense of classical model theory iff its Morleyization is complete in the sense of geometric logic.
Olivia Caramello, Atomic toposes and countable categoricity , Appl. Cat. Struc. 20 no. 4 (2012) pp.379-391. (arXiv:0811.3547)
C. C. Chang, H. J. Keisler, Model theory , North-Holland Amsterdam 1973.
Created on June 14, 2020 at 21:14:59. See the history of this page for a list of all contributions to it.