Naive set theory for the mathematical topic. Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of naive set theory. After the discovery...

combinations of sets Naive set theory – Informal set theories Symmetric difference – Elements in exactly one of two sets Union (set theory) – Set of elements...

generators. The paradoxes of naive set theory can be explained in terms of the inconsistent tacit assumption that "all classes are sets". With a rigorous foundation...

discovery of paradoxes in naive set theory, such as Russell's paradox, led to the desire for a more rigorous form of set theory that was free of these paradoxes...

Russell's paradox. The term "naive set theory" is used in various ways. In one usage, naive set theory is a formal theory, that is formulated in a first-order...

the set of ground facts in the program, then repeatedly add consequences of the rules until a fixpoint is reached. This algorithm is called naïve evaluation...

in naive set theory, which shows that there cannot exist a "set of all sets" or "universe set". It starts by assuming there is some set of all sets, U...

In statistics, naive (sometimes simple or idiot's) Bayes classifiers are a family of "probabilistic classifiers" which assumes that the features are conditionally...

mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine...

Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax)...

Stoll, Robert R. (1963). Set Theory and Logic. San Francisco, CA: Dover Publications. ISBN 978-0-486-63829-4. {{cite book}}: ISBN / Date incompatibility...

empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure...

have an order type Ω {\displaystyle \Omega } . It is easily shown in naïve set theory (and remains true in ZFC but not in New Foundations) that the order...

paradox in naïve set theory. naive set theory 1.  Naive set theory can mean set theory developed non-rigorously without axioms 2.  Naive set theory can mean...

and set theory at the turn of the 20th century, like Russell's paradox. This third aim motivated the adoption of the theory of types in PM. The theory of...

computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: What...

Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness...

Morse–Kelley set theory. (Note that every ZFC model is also a ZF model, and every ZF model is also a Z model.) V is not "the set of all (naive) sets" for two...

University Press, pp. 7–37 Halmos, Paul (1960). Naive Set Theory R. Springer. p. 28. ISBN 9780387900926. {{cite book}}: ISBN / Date incompatibility (help) Lucas...

new phase when Georg Cantor in 1874 introduced what is now called naive set theory and used it as a base for his work on transfinite numbers. When paradoxes...

in set theory, the constructible universe (or Gödel's constructible universe), denoted by L , {\displaystyle L,} is a particular class of sets that...

Naïve. Super. (Original title: Naiv.Super.) is a novel by the Norwegian author Erlend Loe. It was first published in 1996 in Norwegian, and proved to...

Foundations and positive set theory use different restrictions of the axiom of comprehension of naive set theory. The Alternative Set Theory of Vopenka makes...

Coquand's Calculus of Inductive Constructions. Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which...

Theory of Fiction is the most famous work of the literary scholar Frank Kermode. It was first published in 1967 by Oxford University Press. The book originated...

class of formal systems, some of which can serve as alternatives to naive set theory as a foundation for all mathematics. It has been tied to formal mathematics...

Kunen, Kenneth, 1980. Set Theory: An Introduction to Independence Proofs. Elsevier. ISBN 0-444-86839-9. Paul Halmos, Naive set theory. Princeton, NJ: D....

Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces...