Topic
Equinumerosity
About: Equinumerosity is a research topic. Over the lifetime, 339 publications have been published within this topic receiving 6803 citations. The topic is also known as: equipollence & equipotence.
Papers published on a yearly basis
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Papers
Book•
19 Jul 1990
TL;DR: Polymorphic sets: the semantics of the judgement forms general rules enumeration sets Cartesian product of a family of sets equality sets natural numbers lists cartesian product two sets disjoint union of two sets Disjoint Union of small sets (the first universe) well-orderings general trees.
Abstract: Part 1 Polymorphic sets: the semantics of the judgement forms general rules enumeration sets Cartesian product of a family of sets equality sets natural numbers lists cartesian product of two sets disjoint union of two sets disjoint union of a family of sets the set of small sets (the first universe) well-orderings general trees. Part 2 Subsets: subsets in the basic set theory the subset theory. Part 3 Monomorphic sets: types defining sets in terms of types. Part 4 Examples: some small examples program derivation specification of abstract data types.
573 citations
1 Jan 1990
TL;DR: The first part of the axiomatics of the Mizar system is presented in this paper. But it does not include the axioms of the Tarski Grothendieck set theory.
Abstract: This is the first part of the axiomatics of the Mizar system. It includes the axioms of the Tarski Grothendieck set theory. They are: the axiom stating that everything is a set, the extensionality axiom, the definitional axiom of the singleton, the definitional axiom of the pair, the definitional axiom of the union of a family of sets, the definitional axiom of the boolean (the power set) of a set, the regularity axiom, the definitional axiom of the ordered pair, the Tarski’s axiom A introduced in [1] (see also [2]), and the Fraenkel scheme. Also, the definition of equinumerosity is introduced.
514 citations
TL;DR: The concepts of soft set relations are introduced as a sub soft set of the Cartesian product of the soft sets and many related concepts such as equivalent soft set relation, partition, composition, function etc are discussed.
Abstract: The traditional soft set is a mapping from a parameter to the crisp subset of universe. Molodtsov introduced the theory of soft sets as a generalized tool for modeling complex systems involving uncertain or not clearly defined objects. In this paper the concepts of soft set relations are introduced as a sub soft set of the Cartesian product of the soft sets and many related concepts such as equivalent soft set relation, partition, composition, function etc. are discussed.
359 citations
Book•
22 Jun 1999
TL;DR: Sets relations, functions and orderings natural numbers finite, countable and uncountable sets cardinal numbers ordinal numbers alephs the axiom of choice arithmetic of cardinal numbers sets of real numbers filters and ultrafilters combinatorial set theory large cardinals the axiomatic set theory as discussed by the authors
Abstract: Sets relations, functions and orderings natural numbers finite, countable and uncountable sets cardinal numbers ordinal numbers alephs the axiom of choice arithmetic of cardinal numbers sets of real numbers filters and ultrafilters combinatorial set theory large cardinals the axiom of foundation the axiomatic set theory.
350 citations
Book•
30 Oct 2012
TL;DR: A list of axioms and operations for the algebra of sets can be found in this paper, where the authors also provide a discussion of the relation between the Axiom of Choice Equinumerosity Finite Sets and cardinal numbers.
Abstract: Contents Preface List of Symbols Chapter 1 Introduction Baby Set Theory Sets-An Informal View Classes Axiomatic Method Notation Historical Notes Chapter 2 Axioms and Operations Axioms Arbitrary Unions and Intersections Algebra of Sets Epilogue Review Exercises Chapter 3 Relations and Functions Ordered Pairs Relations n-Ary Relations Functions Infinite Cartesian Products Equivalence Relations Ordering Relations Review Exercises Chapter 4 Natural Numbers Inductive Sets Peano's Postulates Recursion on Arithmetic Ordering on Review Exercises Chapter 5 Construction of the Real Numbers Integers Rational Numbers Real Numbers Summaries Two Chapter 6 Cardinal Numbers and the Axiom of Choice Equinumerosity Finite Sets Cardinal Arithmetic Ordering Cardinal Numbers Axiom of Choice Countable Sets Arithmetic of Infinite Cardinals Continuum Hypothesis Chapter 7 Orderings and Ordinals Partial Orderings Well Orderings Replacement Axioms Epsilon-Images Isomorphisms Ordinal Numbers Debts Paid Rank Chapter 8 Ordinals and Order Types Transfinite Recursion Again Alephs Ordinal Operations Isomorphism Types Arithmetic of Order Types Ordinal Arithmetic Chapter 9 Special Topics Well-Founded Relations Natural Models Cofinality Appendix Notation, Logic, and Proofs Selected References for Further Study List of Axioms Index
327 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2018 | 1 |
| 2017 | 7 |
| 2016 | 12 |
| 2015 | 7 |
| 2014 | 11 |