Definition of Axiomatize. Meaning of Axiomatize. Synonyms of Axiomatize

- In 1936, Alfred Tarski gave an axiomatization of the real numbers and their arithmetic, consisting of only the eight axioms shown below and a mere four...
- the standard ZFC axiomatization of set theory. Czesław Ryll-Nardzewski proved that Peano arithmetic cannot be finitely axiomatized, and Richard Montague...
- there are certain consistent bodies of propositions with no recursive axiomatization. Typically, the computer can recognize the axioms and logical rules...
- impossible to axiomatize ZFC using only finitely many axioms. On the other hand, von Neumann–Bernays–Gödel set theory (NBG) can be finitely axiomatized. The ontology...
- a modern treatment of Euclidean geometry. Other well-known modern axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff...
- self-evident in nature (e.g., the parallel postulate in Euclidean geometry). To axiomatize a system of knowledge is to show that its claims can be derived from a...
- is a complemented distributive lattice. The section on axiomatization lists other axiomatizations, any of which can be made the basis of an equivalent definition...
- Sanders Peirce provided an axiomatization of natural-number arithmetic. In 1888, Richard Dedekind proposed another axiomatization of natural-number arithmetic...
- previous work by Pasch. The success in axiomatizing geometry motivated Hilbert to s**** complete axiomatizations of other areas of mathematics, such as...
- (compact totally disconnected Hausdorff) topological space. The first axiomatization of Boolean lattices/algebras in general was given by the English philosopher...