The Algebra of Logic
by Louis Couturat
Publisher: Project Gutenberg 2004
Number of pages: 102
Mathematical Logic is a necessary preliminary to logical Mathematics. The present work is concerned with the "calculus ratiocinator" aspect, and shows, in an admirably succinct form, the beauty, symmetry and simplicity of the calculus of logic regarded as an algebra.
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by Edward Nelson - Princeton Univ Pr
The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.
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Russell's classic sets forth his landmark thesis that mathematics and logic are identical -- that what is called mathematics is simply later deductions from logical premises. His ideas have had a profound influence on the foundations of mathematics.
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This text treats pure logic and in this connection introduces to basic proof-theoretic techniques. Fundamentals of model theory and those of recursion theory are dealt with. Furthermore, some extensions of first order logic are treated.
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