Mathematical Logic by Roman Kossak

Author:Roman Kossak
Language: eng
Format: epub, pdf
ISBN: 9783319972985
Publisher: Springer International Publishing

7.4 Definability: New Relations from Old

Now, after crucial definitions have been introduced, we can begin to explore the world of structures. In various branches of mathematics, the study of either specific structures or the whole classes of them, has evolved into an art form involving advanced techniques applied at lofty levels of abstraction. What I am going to describe here is a small portion of those efforts that does not require anything too advanced. All we need is familiarity with the formalism of the first-order logic, in particular the important concept of definability that we have already discussed informally, and which now will be defined precisely. As we introduce more structures and other mathematical objects, we quickly run out of symbols to denote them. It is an old tradition in mathematical logic to use the German Fraktur font to denote structures. We will follow this tradition.

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