Search for "Set theory" in article titles:

1. Set theory: Set theory is a branch of mathematics dealing with collections of objects, called sets. It revolutionized mathematics and made possible enormous new insights. [100%] 2023-02-23 [Set Theory]
2. Set theory: Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly ... (Branch of mathematics that studies sets) [100%] 2024-01-04 [Set theory] [Mathematical logic]...
3. Set theory: Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly ... (Branch of mathematics that studies sets) [100%] 2024-01-04 [Set theory] [Mathematical logic]...
4. Set theory: A set, in mathematics, is a collection of distinct entities, called its elements, considered as a whole. The early study of sets led to a family of paradoxes and apparent contradictions. [100%] 2023-07-06
5. Set theory: naive Set theory is the study of the properties of sets (cf. Set) by themselves, disregarding the properties of their elements. (Mathematics) [100%] 2023-12-17
6. Set theory: The term "set" can be thought as a well-defined collection of objects. In set theory, These objects are often called "elements". [100%] 2024-01-04 [Set theory]
7. Set theory: naive Set theory is the study of the properties of sets (cf. Set) by themselves, disregarding the properties of their elements. (Mathematics) [100%] 2024-03-08
8. Set theory and the Bible: Set theory and the Bible is an approach that seeks to understand both mathematics and the Bible by viewing them through set theory. Georg Cantor championed this approach as a way of understanding eternity in the Bible, an his work ... [63%] 2023-02-27 [Bible] [Mathematics]...
9. Set theory of the real line: Set theory of the real line is an area of mathematics concerned with the application of set theory to aspects of the real numbers. For example, one knows that all countable sets of reals are null, i.e. [57%] 2023-02-18 [Set theory]
10. Set Theory: Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. Pure set theory deals exclusively with sets, so the only sets under consideration are those whose members ... (Philosophy) [100%] 2021-12-24
11. Filter (set theory): In mathematics, a filter on a set \displaystyle{ X }[/math] is a family \displaystyle{ \mathcal{B} }[/math] of subsets such that: A filter on a set may be thought of as representing a "collection of large subsets", one intuitive example ... (Set theory) [81%] 2023-12-20 [General topology] [Order theory]...
12. General set theory: General set theory (GST) is George Boolos's (1998) name for a fragment of the axiomatic set theory Z. GST is sufficient for all mathematics not requiring infinite sets, and is the weakest known set theory whose theorems include the ... (System of mathematical set theory) [81%] 2023-09-21 [Systems of set theory]
13. Finitist set theory: Finitist set theory (FST) is a collection theory designed for modeling finite nested structures of individuals and a variety of transitive and antitransitive chains of relations between individuals. Unlike classical set theories such as ZFC and KPU, FST is not ... [81%] 2023-09-23 [Set theory] [Constructivism (mathematics)]...
14. Ideal (set theory): In the mathematical field of set theory, an ideal is a partially ordered collection of sets that are considered to be "small" or "negligible". Every subset of an element of the ideal must also be in the ideal (this codifies ... (Set theory) [81%] 2024-01-12 [Set theory]
15. Named set theory: Named set theory is a branch of theoretical mathematics that studies the structures of names. The named set is a theoretical concept that generalizes the structure of a name described by Frege. [81%] 2023-12-20 [Set theory]
16. Constructive set theory: Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language with " = {\displaystyle =} " and " ∈ {\displaystyle \in } " of classical set theory is usually used, so this is not to be ... (Axiomatic set theories based on the principles of mathematical constructivism) [81%] 2023-12-24 [Constructivism (mathematics)] [Intuitionism]...
17. Axiomatic set theory: The branch of mathematical logic in which one deals with fragments of the informal theory of sets by methods of mathematical logic. Usually, to this end, these fragments of set theory are formulated as a formal axiomatic theory. (Mathematics) [81%] 2024-01-04
18. Descriptive set theory: The branch of set theory whose subject is the study of sets in dependence of those operations by which these sets may be constructed from relatively simple sets (e.g. closed or open subsets of a given Euclidean, metric or ... (Mathematics) [81%] 2023-10-19
19. Positive set theory: In mathematical logic, positive set theory is the name for a class of alternative set theories in which the axiom of comprehension holds for at least the positive formulas \displaystyle{ \phi }[/math] (the smallest class of formulas containing atomic membership ... (Class of alternative set theories) [81%] 2023-09-21 [Systems of set theory]
20. Zermelo set theory: Zermelo set theory (sometimes denoted by Z), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory (ZF) and its extensions, such as von Neumann–Bernays–Gödel set theory ... (System of mathematical set theory) [81%] 2023-09-21 [Systems of set theory]
21. Union (set theory): In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. (Set theory) [81%] 2023-09-01 [Boolean algebra] [Basic concepts in set theory]...
22. Pocket set theory: Pocket set theory (PST) is an alternative set theory in which there are only two infinite cardinal numbers, ℵ0 (aleph-naught, the cardinality of the set of all natural numbers) and c (the cardinality of the continuum). The theory was ... (Alternative mathematical set theory) [81%] 2024-01-04 [Systems of set theory]
23. Conglomerate (set theory): In mathematics, a conglomerate is a collection of classes, just as a class is a collection of sets. A quasi-category is like a category except that its objects and morphisms form conglomerates instead of classes. (Set theory) [81%] 2023-10-17 [Higher category theory] [Set theory]...
24. Multiverse (set theory): In mathematical set theory, the multiverse view is that there are many models of set theory, but no "absolute", "canonical" or "true" model. The various models are all equally valid or true, though some may be more useful or attractive ... (Set theory) [81%] 2023-11-23 [Set theory] [Philosophy of mathematics]...
25. Morass (set theory): In axiomatic set theory, a mathematical discipline, a morass is an infinite combinatorial structure, used to create "large" structures from a "small" number of "small" approximations. They were invented by Ronald Jensen for his proof that cardinal transfer theorems hold ... (Set theory) [81%] 2023-11-29
26. Filter (set theory): In mathematics, a filter on a set X {\displaystyle X} is a family B {\displaystyle {\mathcal {B}}} of subsets such that: A filter on a set may be thought of as representing a "collection of large subsets", one intuitive example ... (Set theory) [81%] 2023-08-31 [General topology] [Order theory]...
27. Uniformization (set theory): In set theory, a branch of mathematics, the axiom of uniformization is a weak form of the axiom of choice. It states that if \displaystyle{ R }[/math] is a subset of \displaystyle{ X\times Y }[/math], where \displaystyle{ X }[/math ... (Set theory) [81%] 2023-12-28 [Set theory] [Descriptive set theory]...
28. Internal set theory: Internal set theory (IST) is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the nonstandard analysis introduced by Abraham Robinson. Instead of adding new elements to the real numbers, Nelson ... (System of mathematical set theory) [81%] 2024-01-04 [Systems of set theory] [Nonstandard analysis]...
29. Morass (set theory): In axiomatic set theory, a mathematical discipline, a morass is an infinite combinatorial structure, used to create "large" structures from a "small" number of "small" approximations. They were invented by Ronald Jensen for his proof that cardinal transfer theorems hold ... (Set theory) [81%] 2023-12-03 [Trees (set theory)]
30. Complement (set theory): In set theory, the complement of a set A, often denoted by A ∁ {\displaystyle A^{\complement }} (or A′), is the set of elements not in A. When all elements in the universe, i.e. (Set theory) [81%] 2024-02-05 [Basic concepts in set theory] [Operations on sets]...
31. Set point theory: Set point theory, as it pertains to human body weight, states that there is a biological control method in humans that actively regulates weight towards a predetermined set weight for each individual. This may occur through regulation of energy intake ... (Theory in human biology) [81%] 2023-10-28 [Human body weight] [Weight loss]...
32. Naive set theory: 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 defined using formal logic, naive set theory is defined informally, in natural language. (Informal set theories) [81%] 2023-09-23 [Set theory] [Systems of set theory]...