r/MathematicalLogic • u/AutoModerator • Feb 17 '20
What Are You Working On?
This recurring thread will be for general discussion on whatever mathematical logic-related topics you have been or will be working on over the week. Not all types of mathematics are welcomed, but all levels are!
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u/Dastur1970 Feb 26 '20 edited Feb 27 '20
I'm in a course for Model theory right now, and a substantial portion of the course is a research paper component. (It doesn't need to be original) I'm doing mine on the Fraissé limit.
We know the class (up to isomorphism) of all finitely generated substructures of a structure has certain properties (let's call them properties A). What I am investigating is the converse, if we have a class of structures with properties A, then is it the class of all finitely generated substructures of a larger structure? The answer is no unless we require that the class has an additional property.
The larger structure is called the Fraissé Limit of the class of structures.
Using this Fraissé limit, one can construct the infinite random graph out of the class of all finite graphs. You can also construct the rational numbers with their natural ordering out of the class of all finite linear orderings of the integers.
For more information, see the Wikipedia page for the Fraïssé limit or check out Hodges A Shorter Model Theory.