# Questions tagged [ordinal-numbers]

An ordinal is the order type of a well-ordered set. The first few ordinals are $0, 1, 2, \dots, \omega, \omega+1, \dots$ where $\omega$ is the order type of $\mathbb{N}$, and $\omega+1$ is the order type of $\mathbb{N}$ together with a maximum element.

**0**

**0**answers

### Cantor normal form [closed]

**4**

**1**answer

### How to compare three supremums of ordinals eventually writable by Ordinal Turing Machines?

**4**

**2**answers

### How large is the supremum of halting times of Infinite Time Turing Machines, assuming that halting times are bounded and inputs are arbitrary?

**3**

**1**answer

### Ordinal numbers reachable by primitive recursive ordinal functions in omega

**3**

**1**answer

### Cardinality of infinite towers of Alephs - can tower be more than countable?

**14**

**2**answers

### Definability of Gödel's pairing function on ordinals

**0**

**1**answer

### What comes after the Bachmann Howard Ordinal?

**2**

**0**answers

### Countable Fodor's Lemma?

**1**

**1**answer

### How large is the smallest ordinal larger than any “minimal ordinal parameter” for any pair of an Ordinal Turing Machine and a real?

**3**

**1**answer

### Where can I read about Veblen functions / klammersymbols beyond the large Veblen ordinal?

**5**

**0**answers

### Higher order arithmetic, hierarchies and proof theoretic ordinals

**5**

**1**answer

### Definability of ordinals in various signatures

**3**

**0**answers

### Trees of prescribed ordinal

**11**

**1**answer

### Intuition about ordinal fixed points $\alpha = \aleph_\alpha$

**3**

**0**answers

### Self-contained proof of WO of Buchholz's ordinal notation system

**6**

**1**answer

### For which ordinals do we have $V_\alpha = L_\alpha$?

**3**

**1**answer

### A connected topological space whose points cannot be connected by irreducible components

**2**

**2**answers

### Veblen function with uncountable ordinals & beyond

**9**

**1**answer

### Does every cofinal branch through Kleene's O compute true arithmetic?

**3**

**1**answer

### From a constructive perspective, what are the ordinal numbers?

**16**

**1**answer

### Has the exponentiation of ordinals a nice geometric model?

**6**

**1**answer

### Is Axiom of Choice equivalent to its version for families of sets, indexed by ordinals? [duplicate]

**4**

**0**answers

### Infinite positions in 3D chomp

**10**

**2**answers

### Transfinite algorithms

**22**

**4**answers

### What's the use of countable ordinals? (prompted by a remark of Tim Gowers)

**5**

**1**answer

### How far does this restricted definition on $\mathcal{O}$ goes?

**5**

**0**answers

### $Π_2$ strength of KP

**0**

**1**answer

### Can I find the definition of Jager's ordinal collapsing functions?

**10**

**1**answer

### Examples of proofs using induction or recursion on a big recursive ordinal

**2**

**0**answers

### Smallest ordinal modelling $\aleph_1$?

**6**

**0**answers

### What is proof-theoretic ordinal of weak first-order arithmetic?

**5**

**1**answer

### Club filter basis in $\omega_1$

**4**

**1**answer

### Which ordinal is larger, the supremum of ordinals writable by iterated Infinite Time Turing Machines or the smallest $\Sigma_2^1$-reﬂecting ordinal?

**12**

**0**answers

### Is it an open problem whether fast-growing hierarchies can be defined without fundamental sequences?

**2**

**1**answer

### Relation between $\eta$ and $\omega^L_1$

**0**

**2**answers

### Why do ordinal collapsing functions use regular cardinals?

**5**

**0**answers

### Weaker versions of Gandy ordinals

**4**

**3**answers

### Compact definition of ordinals

**9**

**1**answer

### Computable models of the ordinal numbers

**2**

**1**answer

### Generalizing König's Lemma

**5**

**1**answer

### Capturing the $\omega_1^{\mathrm{CK}}$-th stage of Gödel's constructible hierarchy

**-6**

**1**answer

### Is the least ordinal containing all countable ordinals defined by a formula an element of itself? (Out of date, see below)

**2**

**0**answers

### Coloring triples in trees

**4**

**1**answer

### Function on the set of limit countable ordinals

**3**

**0**answers

### Simple transfinite generalization of $p$-adic integers

**1**

**1**answer

### Countable union of well ordered sets [closed]

**1**

**1**answer

### An Apparent Incongruity

**3**

**0**answers

### Partial well-ordering of formulas

**3**

**1**answer

### Hartogs' Number of the Reals and $\Theta$ without choice

**1**

**0**answers