indiscernible sequence?
Morley sequence?
Ramsey theorem?
Erdos-Rado theorem?
Ehrenfeucht-Fraïssé games (back-and-forth games)
Hrushovski construction?
generic predicate?
The concept of an institution provides an abstract category-theoretic rendering of the informal concept of a logical system. It was introduced by Burstall and Goguen in the 1970s in order to get a grip on the proliferation of specification logics in programming and constitutes a genuine contribution of theoretical computer science to general logic and abstract model theory.
An institution is a quadruple $\langle\Sigma , S, M, \models\rangle$ with
$\Sigma$ a category of “signatures”,
$S:\Sigma\to Set$ a functor assigning to an object $X\in \Sigma$ the set $S(X)$ of “sentences” of signature $X$ ,
$M:\Sigma^{op} \to Cat$ is a functor assigning to an object $X\in\Sigma^{op}$ the category of “X-structures” and
$\models$ is a family of “satisfaction” relations specifying for each signature $X$ and $X$-structure $\mathfrak{A}$ the set of sentences $Th(\mathfrak{A})\subseteq S(X)$ “holding in $\mathfrak{A}$”,
subject to the following satisfaction condition:
Given a morphism of signatures $\varphi:X\to X'$ and a sentence $e\in S(X)$, the sentence $S(\varphi)(e)$ i.e. the “$\varphi$-translation” of $e$ into an $X'$-sentence, holds in a X’-structure $\mathfrak{A}'$ (in signs: $\mathfrak{A}'\models S(\varphi)(e)$) precisely if $e$ holds in $M(\varphi)(\mathfrak{A}')$:
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The late Joseph Goguen’s page on institutions.
A Bremen based community homepage: Flirts.
One of the original sources is
A high level introduction
A monograph on the subject is
More specific research papers are
M. Aiguier, F. Barbier, An institution-independent Proof of the Beth Definability Theorem , Studia Logica 85 no. 3 (2007) pp.333-359. (pdf)
Răzvan Diaconescu, Grothendieck institutions , App. Cat. Struc. 10 no.4 (2002) pp.383–402.
Lucanu, D., Li, Y. F., & Dong, J. S. (2006). Semantic web languages–towards an institutional perspective. In Algebra, Meaning, and Computation (pp. 99-123). Springer, Berlin, Heidelberg. (pdf)
Bao, J., Tao, J., McGuinness, D. L., & Smart, P. (2010). Context representation for the semantic web. (pdf)
Last revised on March 3, 2021 at 13:03:14. See the history of this page for a list of all contributions to it.