Live briefing
Everything about Ordinal arithmetic
Operations on ordinals that extend classical arithmetic
In the mathematical field of set theory, ordinal arithmetic includes binary operations on ordinal numbers such as addition, multiplication, and exponentiation. Each can be defined in two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by using transfinite recursion. In addition to these standard operations for ordinals, there are also the "natural" arithmetic operations, which are usually described using the Cantor normal form for ordinals, and nimber operations. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Ordinal arithmeticA 5-minute orientation
- Skim a recent paper: Embedding of the First Nonconstructive Ordinal into the Rogers Semilattices of Families of Arithmetic SetsInfluential work since 2022
- Pick up a classic book: The order of thingsThe most-reprinted book on the subject
- Read the landmark paper: Ordinal Arithmetic: Algorithms and MechanizationCited 20 times
- Go sideways: Epsilon numberA closely related topic
- Go sideways: Ordinal collapsing functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Ordinal Arithmetic: Algorithms and Mechanization
Serial order working memory and numerical ordinal processing share common processes and predict arithmetic abilities
Ordinal arithmetic and $\Sigma_{1}$ -elementarity
An extended arithmetic of ordinal numbers
The interplay between spatial ordinal knowledge, linearity of number-space mapping, and arithmetic skills
Ordinal arithmetic based on Skolem hulling
Ordinal notations and well-orderings in bounded arithmetic
Ordinal arithmetic with simultaneously defined theta-functions
🆕 Influential since 2022
Embedding of the First Nonconstructive Ordinal into the Rogers Semilattices of Families of Arithmetic Sets
Distinct ordinal representations mediate the influence of cardinal knowledge on Preschoolers’ arithmetic performance
Construction of Ordinal Numbers and Arithmetic of Ordinal Numbers
The Relationship Between Number Sense and Arithmetic Fluency in 5- to 6-Year-Old Children: The Mediating Role of Ordinal Knowledge
📚 Books worth reading
The order of thingsBarbara L. Webb · 2012
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Epsilon number In mathematics, the epsilon numbers are a collection of transfinite numbers whose defining property is that they are fixed points of an exponential map…
- Ordinal collapsing function In mathematical logic and set theory, an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive…
- Limit ordinal In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there…
- Ordinal number In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite…
- Additively indecomposable ordinal In set theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any β , γ < α {\displaystyle…
- Nimber In mathematics, a nimber, also known as a "Grundy number" (though not to be confused with a Grundy chromatic number, which is also known as a "Grundy number")…
- Buchholz psi functions Buchholz's psi-functions are a hierarchy of single-argument ordinal functions ψν(α) introduced by German mathematician Wilfried Buchholz in 1986. These…
- Ordinal notation In mathematical logic and set theory, an ordinal notation is a partial function mapping the set of all finite sequences of symbols, themselves members…