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