Titlebook: Logic and Structure; Dirk Dalen Textbook 2013Latest edition Springer-Verlag London 2013 Basic model theory.First-order logic with natural

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Introduction,ly for the communication of their results and their problems. While mathematicians have been claiming the greatest possible exactness for their methods, they have been less sensitive as to their means of communication. It is well known that Leibniz proposed to put the practice of mathematical commun

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Propositional Logic,nd syntax. Simple as the language may be, the reader will benefit from the systematic use of inductive and recursive procedures employed in this book. It would be hard and inconvenient to establish important properties of the language with a mathematical precision without recourse to the suitable in

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Predicate Logic,handle important and realistic mathematical structure, e.g. groups, fields, …In order to discuss these structures one needs names (constants for elements) and variables. Furthermore one wants to extend . to .: .(.)∧.(.) to ∀.(.). Similarly for . and .. Again suitable inductive procedures provide the

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Second-Order Logic, allow quantification over subsets of structures. In that case we speak of a “second-order logic”, which is a logic with two kinds of quantifiers: ∀. and ∀.. The accompanying second-order structure has a domain of elements and one of subsets, which does not necessarily comprise all subsets. For thes

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Intuitionistic Logic, take an example: “Euler’s constant is rational or irrational”. This kind of statement is not useful at all, it gives no clue to the real question: “Oh yeah, which one is it then?”. What one needs is an effective logic, which will pick from the disjunction .∨¬. the correct one, and which will produc

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