Links about transfinite ordinals

• Tutorial introductions
  • Ordinal number on Wikipedia
  • Cantor’s Theory of Ordinal and Cardinal Numbers
  • The Ordinal Numbers and Transfinite Induction
  • A Tutorial on Countable Ordinals by Thomas Forster
  • Transfinite Ordinals and Their Notations: For The Uninitiated by Hilbert Levitz
  • Relation between an OCF and an Ordinal Notation
  • David Madore's articles in French
    • Pourquoi les ordinaux me fascinent
    • Nombres ordinaux : une (longue) introduction
    • Petit guide bordélique de quelques ordinaux intéressants
    • Commentaires sur "Les entrées de blog que je n'arrive jamais à écrire"
  • Large Countable Ordinal by John Carlos Baez
    • Part 1
    • Part 2
    • Part 3
  • The Fast Growing Hierarchy
  • A Tutorial Overview of Ordinal Notations, by Jacques Bailhache
  • Videos
    • Extremely Large Numbers
    • Ridiculously Huge Numbers
  
  
• Formal theories of ordinals
  • On the theory of ordinal numbers By Gaisi TAKEUTI
  
  
• Lists of ordinals
  • Pointless Gigantic List of Infinite Numbers
  • Sbiis Saibian's !!! FORBIDDEN LIST !!! of Infinite Numbers
  • A zoo of ordinals, by David Madore
  
  
• General presentation of ordinal notations
  • Ordinal notation on Googology wiki
  
  
• Web sites about large numbers and ordinals
  • Googology
  • Traveling to the infinity
  • Steps Toward Infinity!
  • Cantor's Attic
  
  
• Fundamental sequences
  • List of systems of fundamental sequences
  
  
• Articles about some ordinal notations
  • Veblen functions
    • Wikipedia
    • CONTINUOUS INCREASING FUNCTIONS OF FINITE AND TRANSFINITE ORDINALS, by Oswald Veblen
    • Fundamental sequences
    • Discussion about Veblen functions on Physics Forums
  • Simmons notation
    • Generating ordinal notations from below with a non-recursive construction of the Schütte brackets
    • Fruitful and helpful ordinal functions
    • A short introduction to Ordinal Notations
    • Other articles
  • Ordinal trees and diagrams
    • Examples by David Madore
    • Ordinal diagrams, by Gaisi Takeuti
  • Madore's collapsing function
    • Wikipedia
  • Buchholz collapsing function
    • Wikipedia
    • A survey on ordinal notations around the Bachmann-Howard ordinal
  • Feferman Theta function
    • Fundamental sequences
  • Hypcos theta function
    • Fundamental sequences
  • Ordinal notations based on a hierarchy of inaccessible cardinals by Wolfram Pohlers
  • Jäger's collapsing functions and ρ-inaccessible ordinals
  • Ordinal Notations Based on a Weakly Mahlo Cardinal by Michael Rathjen
  • Ordinal functions collapsing the least weakly Mahlo cardinal; a system of fundamental sequences
  • Ordinal proof theory of Kripke-Platek set theory augmented by strong reflection principles, by Jan-Carl Stegert
  • Taranovsky notation
    • Ordinal notation, complete presentation of the notation by Dmytro Taranovsky
    • A New Ordinal Notation System, short presentation of the notation by Taranovsky
    • Introduction to Taranovsky's Ordinal Notation by Nayuta Ito
    • Analysis of Taranovsky's Ordinal Notation with "standard OCFs."
    • Steps Toward Infinity!
    • Fundamental Sequences in Taranovsky's Notation
    • Taranovsky's various ordinal notations
    • Built-from-below with Passthrough
    • Does Taranovsky's system of ordinal notations make sense? (posted in the forum mathoverflow)
    • Petit guide bordélique de quelques ordinaux intéressants
    • Commentaires sur "Les entrées de blog que je n'arrive jamais à écrire"
  • Other notations
    • Making an OCF, attempt 2
    • Large number combinatorics III:Sigma ordinal notation
  
  
• Tree ordinals
  • Ridiculously Huge Numbers (Part 40)
  • Applicative theories on tree ordinal numbers
  
  
• Cardinals
  • Cardinal number on Wikipedia
  • Reflective Cardinals, by Dmytro Taranovsky
  • Force to change large cardinal strength, by Erin Carmody
  • Inaccessible cardinal on Cantor's Attic
  • Weakly inaccessible cardinals by Deedlit on xkcd
  • Up to a weakly compact cardinal on Googology
  • Weakly inaccessible ordinals in Introduction to Mathematical Logic
  • if k is weakly inaccessible, then it is the k-th aleph fixed point
  • Mahlo cardinal Google search
  • Hyper inaccessible cardinal Google search
  • Hyper-inaccessible cardinals in StackExchange
  • Inaccessible cardinal on Wikipedia
  • Mahlo and hyper-inaccessible cardinals in StackExchange
  • Inaccessible cardinals in A Tour Through Mathematical Logic by Robert S. Wolf
  • List of large cardinal properties in Wikipedia
  • Diagrams of large cardinals properties
  • The Higher Infinite by Akihiro Kanamori
  • Set Theory 292B: An Ideal Characterization of Mahlo Cardinals by Ting Zhang
  
  
• Proof theory, ordinal analysis and reflection
  • Reverse Mathematics by Antonio Montalban
  • The Foundations of Mathematics by Kenneth Kunen
  • Metatheory and Reflection in Theorem Proving: A Survey and Critique by John Harrison
  • Penrose’s G¨odelian argument by Solomon Feferman
  • Systems of logic based on ordinals by Alan Turing
  • The Art of Ordinal Analysis by Michael Rathjen
  • The Realm of Ordinal Analysis by Michael Rathjen
  • Petit guide bordélique de quelques ordinaux intéressants
  • Is there a computable ordinal encoding the proof strength of ZF? Is it knowable? posted in forum mathoverflow
  • Why isn't this a computable description of the ordinal of ZF? posted in forum mathoverflow
  • Transfinite reflection principles and subsystems of second-order arithmetic by David Fernandez-Duque
  • On Reflection Principles by Peter Koellner
  • A simplified ordinal analysis of first-order reflection by Toshiyasu Arai
  • A sneak preview of proof theory of ordinals by Toshiyasu Arai
  • An Introduction to Reverse Mathematics by John Cobb
  • A Note on Iterated Consistency and Infinite Proofs by Anton Freund
  • On the inevitability of the consistency operator by James Walsh
  • On the inevitability of the consistency operator by Antonio Montalbán and James Walsh
  
  
• Articles about different topics related to ordinals
  • Connecting the Two Worlds: Well-partial-orders and Ordinal Notation Systems, by Jeroen Van der Meeren
  • From a Flexible Type System to Metapredicative Wellordering Proofs by Florian Ranzi
  • Provably computable functions and the Fast Growing Hierarchy by Wilfried Buchholz and Stan Wainer
  • On the Uniqueness Problem for Notations of Recursive Ordinals by Matthew Timothy Wright
  
  
• Forums
  • xkcd
  
  
• Googology
  • Relation between an OCF and an Ordinal Notation
  • General fundamental sequences for OCFs
  • Guideline on How to Use Large Cardinals for Ordinal Notations
  • Creating an OCF based on any function from ordinals to ordinals
  • Are there ordinal hierarchies without fundamental sequences?
  • What is the greatest ordinal notation now?
  • Buchholz's FS system
  • SOA's ordinal
  • Pi-w-reflection - Discussion
  • Full References of Arguments on Ordinal Notations with Large Cardinals
  • Analysis of 非想非非想 notation
  • Ordinal Notation with the PTO of ZFC
  • Fundamental sequences for DON
  • The attempt to make my own ordinals collapse function
  • Not Taranovsky's C
  • An extremely fast-growing OCF
  • Making an OCF, attempt 2
  • My OCF vs standard ordinal notation
  • About Taranovsky Ordinal Notation
    • Taranovsky's various ordinal notations
    • Built-from-below with Passthrough
    • Introduction to Taranovsky's Ordinal Notation
    • Built-from-below in Python
    • Analysis of Taranovsky's C
    • Traditional OCF definition for TON
    • Fundamental Sequences in Taranovsky's Notation
    • Analysis of Taranovsky's Ordinal Notation with "standard OCFs."
    • Second Order Arithmetic Subsystems in Terms of Taranovsky's C
    • Algorithm for Generating LUCOs From TON Expressions + Intuitive Analysis
    • TON, stable ordinals, and my array notation
    • Converting TON Expressions to Sequences
    • DAN not into Taranovsky's notation