Metatheoretical Questions and Methods in Elementary Geometry

Erwin Engeler
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Erwin Engeler: ETH-Zentrum, Mathematikdepartment

Chapter § 3 in Foundations of Mathematics, 1993, pp 54-63 from Springer

Abstract: Abstract The completeness axiom V for plane Euclidean Geometry leaves us facing the problem already considered in Chapter I: In what sense are the sets M and N named in it to be understood? In other words, how to adequately express the content of Axiom V in our formal language? And once more we choose the same solution - we identify sets with extensions of predicates, in the present case with predicates in the first order language of elementary geometry built the basic concepts introduced in § 2. The resulting completeness axiom, made elementary, is called the Tarski Schema.

Date: 1993
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DOI: 10.1007/978-3-642-78052-3_8

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