Foundations of Arithmetic
Although primarily a researcher in geometry, Mario Pieri wrote four papers that addressed aspects of arithmetic: 1906d A Look at the New Logico-Mathematical Direction of the Deductive Sciences 1906e On an Arithmetical Definition of the Irrationals (completed in 1905) 1906g On the Consistency of the Axioms of Arithmetic 1907a On the Axioms of Arithmetic The first three are introduced in the following paragraphs, and will be discussed in detail in the second book of the present series. Section 4.1 presents historical background for the 1906e, 1906g, and 1907a papers. The last, On the Axioms of Arithmetic, is translated in entirety in section 4.2 and discussed in detail in section 4.3.
KeywordsNatural Number Historical Background Underlying Logic Recursive Definition Georg Cantor
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