| 21. | These advances required the late 19th century axiomatization of limits and calculus, which were unavailable to Gauss.
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| 22. | Nowadays alternative approaches for axiomatization of probability theory exist; see Algebra of random variables , for example.
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| 23. | Therefore, no useful axiomatization of set theory can use unrestricted comprehension, at least not with classical logic.
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| 24. | To see this, let ? be a first-order axiomatization of the theory of the real numbers.
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| 25. | The continuous cycles of deterritorialization and reterritorialization through axiomatization makes up one of the basic rhythms of capitalist society.
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| 26. | This is not a first order axiomatization as one of Hilbert's axioms is a second order completeness axiom.
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| 27. | Assume that we have a consistent and complete axiomatization of all true first-order logic statements about natural numbers.
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| 28. | Peano played a key role in the axiomatization of mathematics and was a leading pioneer in the development of mathematical logic.
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| 29. | This axiom schema was tacitly used in the early days of naive set theory, before a strict axiomatization was adopted.
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| 30. | Tarski's axiomatization is shorter than its rivals, in a sense Tarski and Givant ( 1999 ) make explicit.
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