such as the axiom of choice and the law of the excluded middle can be formulated in a manner corresponding to the classical formulation in set theory or perhaps in a spectrum of distinct ways unique to type theory. Some of these principles may be proven to be a consequence of other principles. The variety of formulations of these axiomatic principles allows for a detailed analysis of the formulations required in order to derive various mathematical results. Set theory in mathematical education As set theory gained popularity as a foundation for modern mathematics, there has been support for the idea of introducing the basics of naive set theory early in mathematics education. In the US in the 1960s, the New Math experiment aimed to teach basic set theory, among other abstract concepts, to primary school students, but was met with much criticism. The math syllabus in European schools followed this trend, and currently includes the subject at different levels in all grades. Venn diagrams are widely employed to explain basic set-theoretic relationships to primary school students (even though John Venn originally devised them as part of a procedure to assess the validity of inferences in term logic). Set theory is used to introduce students to logical operators (NOT, AND, OR), and semantic or rule description (technically intensional definition) of sets (e.g. "months starting with the letter A"), which may be useful when learning computer programming, since boolean logic is used in various programming languages. Likewise, sets and other collection-like objects, such as multisets and lists, are common datatypes in computer science and programming. In addition to that, sets are commonly referred to in mathematical teaching when talking about different types of numbers (the sets of natural numbers, of integers, of real numbers, etc.), and when defining a mathematical function as a relation from one set (the domain) to another set (the range). See also Glossary of set theory Class (set theory) List of set theory topics Relational model – borrows from set theory Venn diagram Notes References Further reading External links Daniel Cunningham, Set Theory article in the Internet Encyclopedia of Philosophy. Jose Ferreiros, "The Early Development of Set Theory" article in the [Stanford Encyclopedia of Philosophy]. Foreman, Matthew, Akihiro Kanamori, eds. Handbook of Set Theory. 3 vols., 2010. Each chapter surveys some aspect of contemporary research in set theory. Does not cover established elementary set theory, on which see