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Algebraic systems, relational structures. As considered in model theory, a structure (or a model) is a set endowed with a family of finitary relations and functions (operations). In some contexts, these can be represented by relational structures with some of the $(n+1)$-ary relations being viewed as $n$-ary functions. As considered in universal algebra, an algebraic structure is a structure with operations only.

16 votes
3 answers
1k views

Is there a relational countable ultra-homogeneous structure whose countable substructures do...

Is there a relational countable ultra-homogeneous structure whose countable substructures do not have the amalgamation property? The question can be stated in a fashion not requiring much backgro …
Itaï BEN YAACOV's user avatar
5 votes
1 answer
340 views

Semigroup product of the left-invariant completion of a Polish group (restatement of Questio...

This is a re-statement, of sorts, of the question Is there a relational countable ultra-homogeneous structure whose countable substructures do not have the amalgamation property?, so far unanswered. …
Itaï BEN YAACOV's user avatar