Graduate How is Inaccessible Cardinal Written?

  • Thread starter Thread starter shintashi
  • Start date Start date
  • Tags Tags
    Infinity
Click For Summary
SUMMARY

The discussion centers on the notation for inaccessible cardinals, specifically whether there exists a symbol to represent these concepts in set theory. Participants reference the use of symbols resembling Theta and phi, but no definitive notation is established. The Absolute Infinite, denoted by Ω, is mentioned as a related concept introduced by Georg Cantor, though it is clarified that this symbol does not equate to uncountable or strong inaccessible cardinals. The conversation highlights the philosophical implications of infinity and the challenges in conceptualizing such abstract mathematical ideas.

PREREQUISITES
  • Understanding of set theory concepts, particularly cardinals
  • Familiarity with the notation used in mathematical logic
  • Knowledge of Georg Cantor's contributions to infinity and transfinite numbers
  • Basic grasp of philosophical implications of mathematical concepts, such as noumena
NEXT STEPS
  • Research the notation for inaccessible cardinals in advanced set theory
  • Explore the implications of the Absolute Infinite (Ω) in mathematical philosophy
  • Study the differences between countable, uncountable, and strong inaccessible cardinals
  • Investigate the philosophical concept of noumena and its relation to mathematics
USEFUL FOR

Mathematicians, philosophers of mathematics, and students of set theory seeking to deepen their understanding of cardinal numbers and the notation associated with them.

shintashi
Messages
117
Reaction score
1
I'm writing some notes on set theory, Aleph Null, etc., and was wondering if there's a Notation or Symbol that abbreviates this (inaccessible/strong/uncountable etc. cardinals). I'm not sure if I've seen notation before but it seems like symbols resembling Theta and phi have been used.
 
Physics news on Phys.org
I have been to that wiki article and could not find where it labeled itself symbolically.

Did find this: under this other wiki article: https://en.wikipedia.org/wiki/Absolute_Infinite
"The Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor.

It can be thought as a number which is bigger than any conceivable or inconceivable quantity, either finite or transfinite.
"
However I don't think Cantor or infinite series mathematicians believe the omega from absolute infinite is the same as an uncountable/strong inaccessible cardinal.
Correct me if I am mistaken?
 
I have no expertise in this area. However, the concept of Absolute infinite sounds weird to me. What is Absolute infinity times 2? etc.
 
if it didn't sound weird, how could it possibly be inconceivable? There's a philosophy term for this stuff "Noumenal" stuff we aren't supposed to make sense of.
 

Similar threads

Constructing Structures with Cardinality W2: A Puzzle in Model Theory
  • · Replies 3 ·
Replies
3
Views
2K
Can Strong Induction Prove an Element in Set S Matches Its Own Cardinality?
  • · Replies 8 ·
Replies
8
Views
3K
What is the difference between cardinal and ordinal numbers?
  • · Replies 1 ·
Replies
1
Views
11K
Graduate Summing over continuum and uncountable numerocities
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Choices of Axiomatic and Number Systems / Sets and Alternatives
  • · Replies 2 ·
Replies
2
Views
2K
High School Unbounded Logical Trees: Constructing Natural Numbers with Logical Trees
  • · Replies 7 ·
Replies
7
Views
2K
Natural deduction: True iff not false
  • · Replies 10 ·
Replies
10
Views
2K
Question about Cardinality - Is the Universe One-Dimensional?
  • · Replies 15 ·
Replies
15
Views
6K
What Is the Domain and Cardinality Representation for an Infinite Summation?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Why are General relativity texts so much more formal?
  • · Replies 28 ·
Replies
28
Views
3K