Axiomatizing Changing Conceptions of the Geometric Continuum II: Archimedes-Descartes-Hilbert-Tarski†

Philosophia Mathematica 27 (1):33-60 (2019)
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Abstract

In Part I of this paper we argued that the first-order systems HP5 and EG are modest complete descriptive axiomatization of most of Euclidean geometry. In this paper we discuss two further modest complete descriptive axiomatizations: Tarksi’s for Cartesian geometry and new systems for adding $$\pi$$. In contrast we find Hilbert’s full second-order system immodest for geometrical purposes but appropriate as a foundation for mathematical analysis.

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10.1093/philmat/nkx031

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Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Model theory for infinitary logic.H. Jerome Keisler - 1971 - Amsterdam,: North-Holland Pub. Co..
Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.

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