Coherent, well organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition; Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories in both discussion and exercises. Ideal for undergraduates; no background in math or philosophy required.

Inter-theoretical reduction has always been a major topic in the structuralist philosophy of science. This paper reviews criteria of adequacy which were put forward by Adams, Sneed, Stegmuller, Mayr, Pearce, Kamlah, and Mormann. The criteria are formalized in a simplified structuralist model, and the logical relations between them are investigated. It turns out that various parts of these criteria are incompatible.

The conditions are examined under which one theory is said to be replaceable by another, while preserving those features of the original theory which made it serviceable for a given purpose. Among such replacements, special attention is given to ones which qualify as so-called reductions of a theory, and some theorems are proved concerning the notion of a reduction.

Of the various notions of reduction in the logical literature, relative interpretability in the sense of Tarskiet al. [6] appears to be the central one. In the present note, this syntactic notion is characterized semantically, through the existence of a suitable reduction functor on models. The latter mathematical condition itself suggests a natural generalization, whose syntactic equivalent turns out to be a notion of interpretability quite close to that of Ershov [1], Szczerba [5] and Gaifman [2].