Titlebook: Mathematical Logic; On Numbers, Sets, St Roman Kossak Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), under ex

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Seeing the Number Structuresple answer to this question, and then we will proceed with a reconstruction of the arithmetic structures of the integers and the rational numbers in terms of first-order logic. The reconstruction is technical and rather tedious, but it serves as a good example of how some mathematical structures can

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Set Theorylook at structures in general. The classical number structures fit the definition: a set with a set of relations on it. But what about other structures? Are they all sets? Can a set of relations always be associated with them? Clearly not. Not everything in this world is a set. I am a structured liv

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Definable Elements and Constantsis chapter we will take a look at the smallest nonempty sets—those that have only one element. This a specialized topic, and it is technical, but it will give us an opportunity to see in detail what domains of mathematical structures are made of and in what sense they are “given to us.”

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Tame vs. Wildd mysterious, the latter deceptively simple. As it turns out, as far as the model-theoretic properties are concerned, the roles are reversed, the former is tame while the latter quite wild, and those terms have precise meanings. In recent years, tameness has become a popular word in model theory. Ta

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