User contributions for C7X

31 August 2023

• 22:2722:27, 31 August 2023 diff hist +94‎ Inaccessible cardinal ‎ →‎Strongly inaccessible
• 22:2422:24, 31 August 2023 diff hist −71‎ Constructible hierarchy ‎ →‎Definition
• 22:2022:20, 31 August 2023 diff hist +7‎ Constructible hierarchy ‎ →‎Definition
• 22:2022:20, 31 August 2023 diff hist +31‎ Constructible hierarchy ‎ →‎Definition
• 22:1922:19, 31 August 2023 diff hist +19‎ Constructible hierarchy ‎ How is the reflection principle stated for general cumulative hierarchies?
• 22:1822:18, 31 August 2023 diff hist +8‎ ZFC ‎ May sound like ZF proves Banach-Tarski
• 22:1722:17, 31 August 2023 diff hist +19‎ ZFC ‎ Citation for name needed
• 22:1622:16, 31 August 2023 diff hist +198‎ Ordinal ‎ →‎Ordinal arithmetic
• 10:0010:00, 31 August 2023 diff hist +24‎ Second-order arithmetic ‎No edit summary current
• 06:1206:12, 31 August 2023 diff hist +1,758‎ Ordinal collapsing function ‎ →‎List
• 06:1206:12, 31 August 2023 diff hist +1‎ Patterns of resemblance ‎ →‎Reflection criterion
• 06:0606:06, 31 August 2023 diff hist +87‎ Patterns of resemblance ‎No edit summary
• 06:0506:05, 31 August 2023 diff hist +456‎ Patterns of resemblance ‎No edit summary
• 06:0306:03, 31 August 2023 diff hist −82‎ Patterns of resemblance ‎No edit summary
• 06:0206:02, 31 August 2023 diff hist −19‎ Patterns of resemblance ‎No edit summary
• 05:5805:58, 31 August 2023 diff hist +16‎ Stability ‎No edit summary current
• 05:5705:57, 31 August 2023 diff hist +468‎ Stability ‎ →‎(+η)-stability
• 04:1104:11, 31 August 2023 diff hist +43‎ Ordinal collapsing function ‎ Possibly less confusing wording
• 00:3200:32, 31 August 2023 diff hist +77‎ Gandy ordinal ‎No edit summary current
• 00:3100:31, 31 August 2023 diff hist −14‎ Gandy ordinal ‎ "Diagonalizer" terminology not needed, Taranovsky has given this as an example of an ordinal assignment in DoR
• 00:2900:29, 31 August 2023 diff hist +159‎ Stability ‎No edit summary
• 00:1800:18, 31 August 2023 diff hist +2‎ Mahlo cardinal ‎ →‎Weakly Mahlo
• 00:1000:10, 31 August 2023 diff hist +493‎ Stability ‎No edit summary

30 August 2023

• 23:3623:36, 30 August 2023 diff hist +91‎ Stability ‎ More citation

29 August 2023

• 22:3822:38, 29 August 2023 diff hist 0‎ Patterns of resemblance ‎ →‎Stability
• 22:3822:38, 29 August 2023 diff hist +660‎ Patterns of resemblance ‎No edit summary
• 22:3122:31, 29 August 2023 diff hist +1,037‎ Patterns of resemblance ‎No edit summary
• 22:1822:18, 29 August 2023 diff hist +1,038‎ Patterns of resemblance ‎No edit summary
• 21:5621:56, 29 August 2023 diff hist +130‎ Patterns of resemblance ‎ Stability isn't an ordinal notation
• 21:5121:51, 29 August 2023 diff hist −17‎ Ordinal function ‎ Linking
• 21:5021:50, 29 August 2023 diff hist +43‎ Ordinal ‎ Provable over ZFC (and I'd expect some weaker theories)
• 21:4021:40, 29 August 2023 diff hist +813‎ N Gap ordinal ‎ Created page with "A gap ordinal is an ordinal \(\alpha\) such that \((L_{\alpha+1}\setminus L_\alpha)\cap\mathcal P(\omega)=\varnothing\).<ref name="MarekSrebrny73">W. Marek, M. Srebrny, "[https://www.sciencedirect.com/science/article/pii/0003484374900059 Gaps in the Constructible Universe]" (1973). Annals of Mathematical Logic vol. 6, pp.359--394.</ref>^p.364 An ordinal \(\alpha\) is said to start a gap if \(\alpha\) is a gap ordinal but for all \(\beta<\alpha\), \((L_\alpha\se..."
• 21:3321:33, 29 August 2023 diff hist −13‎ List of ordinals ‎No edit summary
• 21:2921:29, 29 August 2023 diff hist +13‎ Sequence system ‎ Possibly clearer wording
• 21:2621:26, 29 August 2023 diff hist −31‎ Fodor's lemma ‎No edit summary current
• 21:2421:24, 29 August 2023 diff hist +518‎ Weakly compact cardinal ‎No edit summary
• 21:1821:18, 29 August 2023 diff hist +68‎ Talk:Weakly compact cardinal ‎ →‎"A relatively convoluted definition" current
• 21:1721:17, 29 August 2023 diff hist +12‎ Talk:Weakly compact cardinal ‎ →‎"A relatively convoluted definition"
• 21:1721:17, 29 August 2023 diff hist +63‎ Talk:Weakly compact cardinal ‎No edit summary
• 21:1521:15, 29 August 2023 diff hist +892‎ N Talk:Weakly compact cardinal ‎ →‎"A relatively convoluted definition": new section Tag: New topic

2 March 2023

• 20:4220:42, 2 March 2023 diff hist +317‎ N Admissible ‎ Created page with "A set \(M\) is admissible if \((M,\in)\) is a model of Kripke-Platek set theory. An ordinal \(\alpha\) is admissible if there exists an admissible set \(M\) such that \(M\cap\textrm{Ord}=\alpha\). This definition of admissibility is equivalent to \(L_\alpha\vDash\textrm{KP}\).<ref>Probably in Barwise somewhere</ref>"
• 20:3920:39, 2 March 2023 diff hist +41‎ Cantor normal form ‎No edit summary

12 January 2023

• 02:3402:34, 12 January 2023 diff hist +144‎ List of ordinals ‎No edit summary
• 02:3302:33, 12 January 2023 diff hist +257‎ List of ordinals ‎No edit summary

29 November 2022

• 02:3302:33, 29 November 2022 diff hist +19‎ Buchholz's psi-functions ‎No edit summary
• 02:3302:33, 29 November 2022 diff hist +1,124‎ N Buchholz's psi-functions ‎ Created page with "Buchholz's \(\psi\)-functions are a family of functions \(\psi_\nu:(\omega+1)\times\textrm{Ord}\to\textrm{Ord},\;\alpha\mapsto\psi_\nu(\alpha)\) defined by Wilfried Buchholz in 1984. ==Historical background== In 1950, H. Bachmann defined the first ordinal collapsing function, Bachmann's \(\varphi\). While able to succinctly describe the Bachmann-Howard ordinal as \(\varphi_{\varepsilon_{\Omega+1}}(0)\), Bachmann's \(\varphi\) had a complicated definition Possible source..."

15 November 2022

• 01:1501:15, 15 November 2022 diff hist +189‎ Ordinal function ‎ Example of Veblen function being defined up to uncountable ordinal Tag: Visual edit

14 November 2022

• 23:5823:58, 14 November 2022 diff hist +52‎ Ordinal function ‎ Some context Tag: Visual edit

16 October 2022

• 02:5502:55, 16 October 2022 diff hist +33‎ Fodor's lemma ‎No edit summary Tag: Visual edit
• 02:5302:53, 16 October 2022 diff hist +1,230‎ N Fodor's lemma ‎ Created page with "'''Fodor's lemma''' (or the '''pressing-down lemma''') is a lemma proven by Géza Fodor in 1956. The lemma states that when \(\kappa\) is an uncountable regular cardinal and \(S\) is a stationary set of ordinals \(<\kappa\), any regressive function \(f:S\to\{<\kappa\}\) must be constant on a stationary set of ordinals \(<\kappa\). ==Importance to apierology== Since \(\omega_1\) is regular, setting \(S=\{<\omega_1\}\), Fodor's lemma implies there does not exist a fundame..."