Titlebook: LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science; Andrea Iacona Textbook 2021 The Editor(s) (if applicable) and The

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Derivability in ,,To say that a formula . is . from a set of formulas Γ in a system S is to say that there is a derivation of . from Γ in S.

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The System ,,This chapter outlines an axiomatic system called .. The language of . is .., the fragment of . whose logical constants are . and ?. So, . may be regarded as an axiomatic version of .., the poor cousin of . considered in Sect. ..

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Consistency, Soundness, Completeness,This chapter deals with three key properties of systems: ., ., and .. As we shall see, . has these three properties, and the same goes for any other system that is deductively equivalent to ., such as ...

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The Language ,,Now .. will be defined in a rigorous way.

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Consistency, Soundness, Completeness,This chapter shows that . is consistent, sound, and complete. The proof methods that will be employed to establish these results are the same that have been employed in Chapter . to prove the consistency, soundness, and completeness of ..

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Undecidability and Related Results,This chapter dwells on some facts about . that concern decidability and related notions.

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