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Would you want to collaborate on an ordinal collapsing function? I was thinking of creating thinning hierarchies consisting of iterated shrewdness diagonalized of degrees of unfoldability, which are in turn diagonalized by ethereal cardinals. If so, how would we collaborate? Should we use Google
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Thanks for the reply. That clears it up for me. My feeling is that it would be better to conclude the proof without introducing an unfamiliar notation. I don't know if the following is a too long-winded replacement for the final sentence: "Then the order
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that the axiom of choice implies the well-ordering theorem. Near the end of the proof there's a notation using angle brackets. Is that a standard notation for ordered set? It might be good to add a brief explanation or a link explaining that.
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Sorry for not seeing this message for a while, I'd be happy to help! I can use Google Docs, although I'm sorry to say I know very little about unfoldable cardinals and elementary embeddings in general
440:. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose 352:. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose 425: 337: 811: 837: 608: 561: 581: 534: 751: 771: 231: 169:. Spread the WikiLove by giving someone else a Mac n' Cheetos, whether it be someone you have had disagreements with in the past or a good friend. 42: 516:
I think I no longer have a copy of the book in the citation, but the notation seems to mean the well-ordering whose length is the supremum of the
66: 73: 227: 479: 391: 842: 711:{\displaystyle \{(a_{\alpha },a_{\beta })\mid a_{\alpha },a_{\beta }\;{\textrm {are}}\;{\textrm {defined}}\land \alpha <\beta \}} 296: 56: 475: 387: 449: 361: 22: 461: 373: 47: 176: 776: 437: 349: 81: 61: 26: 221: 88: 100: 891: 506: 497: 76:, an interactive tour that will help you learn the basics of editing Knowledge (XXG). You can visit the 148: 77: 816: 29:. I hope you like the place and decide to stay. Here are a few links to pages you might find helpful: 212:
Hi. Thank you for your recent edits. An automated process has detected that when you recently edited
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https://docs.google.com/document/d/1J2ThLBQ4PZe9L4MrOpeGhaFEGzovj_icluipIT49GeE/edit?usp=sharing
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Great! I don't 100% understand elementary embeddings myself (I have a vague idea).
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describes the Committee's roles and responsibilities in greater detail.
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describes the Committee's roles and responsibilities in greater detail.
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are allowed to vote. Users with alternate accounts may only vote once.
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are allowed to vote. Users with alternate accounts may only vote once.
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That form sounds fine, I will add it into the article. Thanks!
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Hello, C7XWiki, and welcome to Knowledge (XXG)! Thank you for
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I'm on the googology wikia now under the same username.
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is the panel of editors responsible for conducting the
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is the panel of editors responsible for conducting the
216:, you added a link pointing to the disambiguation page 109: 845: 819: 779: 759: 739: 616: 589: 569: 542: 522: 179:}} to someone's talk page with a friendly message! 878: 831: 805: 765: 745: 710: 602: 575: 555: 528: 175:Spread the goodness of Mac n' Cheetos by adding {{ 208:Disambiguation link notification for September 28 846: 563:is defined, and where the set placed at height 496:A while back you added a proof to the article 610:. The well-ordering itself as a set would be 8: 873: 849: 705: 617: 157:! Mac n' Cheetos is the combination of both 108: 868: 862: 844: 818: 806:{\displaystyle a_{\alpha }<a_{\beta }} 797: 784: 778: 758: 738: 687: 686: 678: 677: 669: 656: 640: 627: 615: 594: 588: 568: 547: 541: 521: 684: 675: 7: 420:2023 Arbitration Committee elections 332:2022 Arbitration Committee elections 438:Knowledge (XXG) arbitration process 404:ArbCom 2023 Elections voter message 350:Knowledge (XXG) arbitration process 316:ArbCom 2022 Elections voter message 48:The five pillars of Knowledge (XXG) 72:You may also want to complete the 14: 832:{\displaystyle \alpha <\beta } 409: 321: 147:(🧀🐆)! Mac n' Cheetos promotes 62:How to create your first article 459:and submit your choices on the 371:and submit your choices on the 43:Contributing to Knowledge (XXG) 646: 620: 252:05:58, 28 September 2021 (UTC) 202:20:13, 23 September 2021 (UTC) 110:ask for help on your talk page 1: 484:00:55, 28 November 2023 (UTC) 396:01:49, 29 November 2022 (UTC) 287:10:21, 26 February 2022 (UTC) 272:17:30, 21 February 2022 (UTC) 918:06:33, 28 January 2024 (UTC) 896:17:16, 26 January 2024 (UTC) 728:22:06, 25 January 2024 (UTC) 511:18:30, 25 January 2024 (UTC) 603:{\displaystyle a_{\alpha }} 556:{\displaystyle a_{\alpha }} 25:, especially your edits to 939: 476:MediaWiki message delivery 388:MediaWiki message delivery 143:Binary198 has given you a 67:Simplified Manual of Style 308:16:13, 1 March 2022 (UTC) 101:Knowledge (XXG):Questions 74:Knowledge (XXG) Adventure 913: 723: 473:to your user talk page. 385:to your user talk page. 282: 197: 576:{\displaystyle \alpha } 529:{\displaystyle \alpha } 123:21:25, 6 May 2021 (UTC) 57:How to develop articles 27:Large countable ordinal 880: 833: 807: 767: 747: 712: 604: 577: 557: 530: 188: 140: 881: 834: 808: 768: 748: 713: 605: 578: 558: 531: 498:Well-ordering theorem 492:Well-ordering theorem 434:Arbitration Committee 417:Hello! Voting in the 346:Arbitration Committee 329:Hello! Voting in the 187: 139: 843: 817: 777: 757: 746:{\displaystyle <} 737: 614: 587: 567: 540: 520: 240:opt-out instructions 177:subst:Mac n' Cheetos 583:in the ordering is 172:'Cheese is tasty' 159:macaroni and cheese 87:Please remember to 876: 829: 803: 763: 743: 708: 685: 676: 600: 573: 553: 526: 450:arbitration policy 362:arbitration policy 230:• Join us at the 189: 154:dangerously cheesy 141: 53:How to edit a page 23:your contributions 871: 766:{\displaystyle A} 690: 681: 486: 398: 235: 222:usually incorrect 220:. 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Thanks, 226:(Read the 93:talk pages 442:site bans 354:site bans 300:Binary198 264:Binary198 163:Frito-Lay 115:Coldtrack 161:and the 149:WikiLove 78:Teahouse 17:Welcome! 910:C7XWiki 720:C7XWiki 689:defined 469:NoACEMM 381:NoACEMM 279:C7XWiki 244:DPL bot 194:C7XWiki 167:Cheetos 536:where 262:Docs? 165:snack 128:Hi C7X 97:tildes 107:, or 914:talk 892:talk 824:< 791:< 741:< 724:talk 700:< 507:talk 480:talk 432:The 392:talk 344:The 304:talk 283:talk 268:talk 257:OCFs 248:talk 198:talk 192:Hi! 119:talk 89:sign 55:and 36:and 886:." 847:sup 753:on 680:are 228:FAQ 916:) 894:) 864:α 856:∣ 853:α 827:β 821:α 799:β 786:α 726:) 703:β 697:α 694:∧ 671:β 658:α 650:∣ 642:β 629:α 596:α 571:α 549:α 524:α 509:) 482:) 471:}} 467:{{ 444:, 394:) 383:}} 379:{{ 356:, 306:) 285:) 270:) 250:) 234:.) 200:) 121:) 84:. 912:( 890:( 874:} 860:a 850:{ 795:a 782:a 761:A 722:( 706:} 667:a 663:, 654:a 647:) 638:a 634:, 625:a 621:( 618:{ 592:a 545:a 505:( 478:( 390:( 302:( 281:( 266:( 246:( 196:( 117:(

Index

your contributions
Large countable ordinal
Introduction
Getting started
Contributing to Knowledge (XXG)
The five pillars of Knowledge (XXG)
How to edit a page
How to develop articles
How to create your first article
Simplified Manual of Style
Knowledge (XXG) Adventure
Teahouse
Task Center
sign
talk pages
tildes
Knowledge (XXG):Questions
my talk page
ask for help on your talk page
Coldtrack
talk
21:25, 6 May 2021 (UTC)

Mac n' Cheetos
WikiLove
dangerously cheesy
macaroni and cheese
Frito-Lay
Cheetos
subst:Mac n' Cheetos

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