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The metamathematics of real numbers can be developed by analysing different formal theories of real numbers. Based on the theory of real closed fields several extensions are investigated proof-theoretically and compared with each other and with other canonical mathematical theories via the relation of interpretability. The results determine the resources employed in those theories and establish a reducibility approach to real numbers.
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Theorien der reellen Zahlen und Interpretierbarkeit, Daniel Alscher
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- 2016
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