User contributions for RhubarbJayde
A user with 299 edits. Account created on 28 August 2023.
30 August 2023
- 20:2920:29, 30 August 2023 diff hist −55 Omega 1 Redirected page to Uncountable Tags: New redirect Visual edit
- 20:2820:28, 30 August 2023 diff hist +394 Admissible No edit summary Tag: Visual edit
- 20:2420:24, 30 August 2023 diff hist +21 Church-Kleene ordinal No edit summary Tag: Visual edit
- 18:0018:00, 30 August 2023 diff hist +237 Reflection principle →Alternate meaning Tag: Visual edit
- 17:5917:59, 30 August 2023 diff hist −1 Reflection principle →Alternate meaning Tag: Visual edit
- 17:5817:58, 30 August 2023 diff hist +4 Reflection principle →Alternate meaning Tag: Visual edit
- 17:5817:58, 30 August 2023 diff hist +1,860 Reflection principle →Alternate meaning Tag: Visual edit
- 17:5517:55, 30 August 2023 diff hist +272 Mahlo cardinal No edit summary Tag: Visual edit
- 17:3717:37, 30 August 2023 diff hist +1,554 Reflection principle No edit summary Tag: Visual edit
- 17:1617:16, 30 August 2023 diff hist +34 N Sound cardinal Redirected page to Reflection principle current Tags: New redirect Visual edit
- 17:1517:15, 30 August 2023 diff hist +34 N Cumulative hierarchy Redirected page to Reflection principle current Tags: New redirect Visual edit
- 17:1517:15, 30 August 2023 diff hist +1,790 N Reflection principle Created page with "The reflection principle is the assertion that properties of the universe of all sets are "reflected" down to a smaller set. Formally, for every formula \(\varphi\) and set \(N\), there is some limit ordinal \(\alpha\) so that, for all \(N \subseteq V_\alpha\), \(x_0, x_1, \cdots, x_n \in V_\alpha\), \(\varphi(x_0, x_1, \cdots, x_n)\) is true in \(V_\alpha\) iff it is really true. This may be considered a guarantee of the existence (be it mathematical or metaphysical) of..." Tag: Visual edit
- 16:5216:52, 30 August 2023 diff hist +2,514 N Kripke-Platek set theory Created page with "Kripke-Platek set theory, commonly abbreviated KP, is a weak foundation of set theory used to define admissible ordinals, which are immensely important in ordinal analysis and \(\alpha\)-recursion theory. In terms of proof-theoretic strength, its proof-theoretic ordinal is the BHO, and it is thus intermediate between \(\mathrm{ATR}_0\) and \(\Pi^1_1 \mathrm{-CA}_0\). The axioms of KP are..." Tag: Visual edit
- 16:3316:33, 30 August 2023 diff hist +61 Buchholz ordinal No edit summary Tag: Visual edit
- 16:3316:33, 30 August 2023 diff hist +35 N Inaccessible ordinal Redirected page to Inaccessible cardinal current Tags: New redirect Visual edit
- 16:3316:33, 30 August 2023 diff hist +48 N Von Neumann ordinal Redirected page to Ordinal#Von Neumann definition current Tags: New redirect Visual edit
- 16:3216:32, 30 August 2023 diff hist +231 Burali–Forti paradox No edit summary Tag: Visual edit
- 16:3116:31, 30 August 2023 diff hist +42 N Limit ordinal Redirected page to Ordinal#Ordinal arithmetic current Tags: New redirect Visual edit
- 16:3016:30, 30 August 2023 diff hist +253 Normal function No edit summary Tag: Visual edit
- 16:2816:28, 30 August 2023 diff hist +41 N Principal Redirected page to Additive principal ordinals current Tags: New redirect Visual edit
- 16:2816:28, 30 August 2023 diff hist −67 Takeuti-Feferman-Buchholz ordinal No edit summary Tag: Visual edit
- 16:2616:26, 30 August 2023 diff hist −108 Omega^omega No edit summary Tag: Visual edit
- 16:2516:25, 30 August 2023 diff hist +4,682 N Second-order arithmetic Created page with "Second-order arithmetic, denoted \(Z_2\) is an extension of first-order (i.e. Peano) arithmetic by adding additional second-order variables as well as an induction scheme for \(\mathcal{P}(\mathbb{N})\), and a comprehension scheme. Proof-theoretically, \(Z_2\) is a very expressive system, as it can prove the consistency of Peano arithmetic and its extensions via the addition of iterated inductive definitions - an ordinal analysis of \(Z_2\) is considered the holy grail o..." Tag: Visual edit
- 15:3415:34, 30 August 2023 diff hist +1 Additive principal ordinals No edit summary Tag: Visual edit
- 15:3415:34, 30 August 2023 diff hist +1,343 N Additive principal ordinals Created page with "An ordinal \(\gamma\) is called an additive principal or additively principal if, for all \(\alpha, \beta < \gamma\), we have \(\alpha+\beta < \gamma). The least additively principal ordinal is 1 since \(0 + 0 = 1\), and all additively principal ordinals other than 1 are limit ordinals. In particular, you can see from the Cantor normal form theorem (every ordinal has a CNF representation) that the additively principal ordinals are precisely the ord..." Tag: Visual edit
- 15:1115:11, 30 August 2023 diff hist +192 Buchholz's psi-functions No edit summary Tag: Visual edit
- 15:0915:09, 30 August 2023 diff hist −2 Buchholz's psi-functions No edit summary Tag: Visual edit
- 15:0815:08, 30 August 2023 diff hist +1,934 Buchholz's psi-functions No edit summary Tag: Visual edit
- 14:5314:53, 30 August 2023 diff hist +41 N OCF Redirected page to Ordinal collapsing function current Tags: New redirect Visual edit
- 14:4814:48, 30 August 2023 diff hist +491 Ordinal collapsing function No edit summary Tag: Visual edit
- 14:4514:45, 30 August 2023 diff hist +1 Ordinal collapsing function →History Tag: Visual edit
- 14:4514:45, 30 August 2023 diff hist +3 Ordinal collapsing function No edit summary Tag: Visual edit
- 14:4414:44, 30 August 2023 diff hist +6,169 N Ordinal collapsing function Created page with "An ordinal collapsing function, typically abbreviated OCF, is a general method of constructing an ordinal representation system, by "collapsing" uncountable or nonrecursive ordinals such as \( \Omega \) or <nowiki>\( \omega_1^{\mathrm{CK}} \)</nowiki> to smaller, recursive ordinals such as the SVO. The primary idea is that, at the point of epsilon numbers and beyond, especially at the level of Stron..." Tag: Visual edit
- 14:0214:02, 30 August 2023 diff hist +28 N Large cardinals Redirected page to Large cardinal current Tags: New redirect Visual edit
- 14:0214:02, 30 August 2023 diff hist +38 N Buchholz's psi Redirected page to Buchholz's psi-functions current Tags: New redirect Visual edit
- 14:0114:01, 30 August 2023 diff hist +38 N Buchholz psi Redirected page to Buchholz's psi-functions current Tags: New redirect Visual edit
- 14:0014:00, 30 August 2023 diff hist +2,538 Gap ordinal No edit summary Tag: Visual edit
- 13:4413:44, 30 August 2023 diff hist +25 N Gap ordinals Redirected page to Gap ordinal current Tags: New redirect Visual edit
- 13:4013:40, 30 August 2023 diff hist +233 Omega^2 No edit summary Tag: Visual edit
- 13:3813:38, 30 August 2023 diff hist +172 Omega^omega No edit summary Tag: Visual edit
- 13:3713:37, 30 August 2023 diff hist +40 List of ordinals No edit summary Tag: Visual edit
- 13:3613:36, 30 August 2023 diff hist +55 List of ordinals No edit summary Tag: Visual edit
- 13:3413:34, 30 August 2023 diff hist +716 N Omega^omega Created page with "The ordinal \( \omega^\omega \) is relatively small compared to other countable ordinals, but has some interesting properties. In particular, \( \omega^\omega \) is: * The least \( \alpha \) so that \( \alpha \) is the \( \alpha \)th limit ordinal. * The least limit of additive principal ordinals. * The least ordinal which is, for all \( n < \omega \), an element of the class \( L^n(\mathrm{Ord}) \), where \( L \) is the limit point operator. * The proof-theoretic ordin..." Tag: Visual edit
- 13:3013:30, 30 August 2023 diff hist +2,007 Mahlo cardinal No edit summary Tag: Visual edit
- 13:1713:17, 30 August 2023 diff hist +4,118 N Mahlo cardinal Created page with "A Mahlo cardinal is a certain type of large cardinal used in the study of reflection principles and consistency strength. These are much stronger than inaccessible cardinals, 1-inaccessible cardinals, hyper-inaccessible cardinals, and more. However, like with inaccessible cardinals, there are two primary types. == Weakly Mahlo == Analogously to how weakly inaccessible cardinals are more popular than strongly inaccessible cardinals in apeirological circles, but less..." Tag: Visual edit
- 12:5012:50, 30 August 2023 diff hist +1 Inaccessible cardinal No edit summary Tag: Visual edit
- 12:4912:49, 30 August 2023 diff hist 0 Inaccessible cardinal No edit summary Tag: Visual edit
- 12:4912:49, 30 August 2023 diff hist +7,527 N Inaccessible cardinal Created page with "There are two main types of notion of inaccessible cardinal - weakly, or strongly inaccessible cardinals. They are the same assuming the generalized continuum hypothesis, but under axioms such as the resurrection axioms, it is possible that the amount of real numbers is weakly inaccessible but, by definition, being very far from being strongly inaccessible. == Weakly inaccessible == Weakly inaccessible cardinals were first invented. Essentially, cardinals such as \( \al..." Tag: Visual edit
- 12:3812:38, 30 August 2023 diff hist +47 N Takeuti-feferman-buchholz ordinal Redirected page to Takeuti-Feferman-Buchholz ordinal current Tags: New redirect Visual edit
- 12:0812:08, 30 August 2023 diff hist +3,877 N Church-Kleene ordinal Created page with "<nowiki>The Church-Kleene ordinal, commonly denoted \( \omega_1^{\mathrm{CK}} \) or \( \omega_1^{ck} \) is defined as the supremum of all "recursive ordinals". A recursive ordinal is the order-type of a well-order on the natural numbers which can be computed by a Turing machine. Note that all countable ordinals are the order-type of a well-order on the natural numbers, but there are only countably many Turing machines, and uncountably many countable ordinals, meaning the..." Tag: Visual edit