About: Omega one of chess

Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Omega one of chess Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

There are a few variants of this ordinal: * If an infinite number of pieces are allowed, the supremum is called \(\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}}\). * With 3D chess, the supremum is called \(\omega_1^{\mathfrak{Ch}_3}\). * With 3D chess with an infinite number of pieces, the supremum is called \(\omega_1^_3}\). This ordinal has been proven to equal the first uncountable ordinal.

Attributes	Values
rdfs:label	Omega one of chess
rdfs:comment	There are a few variants of this ordinal: * If an infinite number of pieces are allowed, the supremum is called \(\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}}\). * With 3D chess, the supremum is called \(\omega_1^{\mathfrak{Ch}_3}\). * With 3D chess with an infinite number of pieces, the supremum is called \(\omega_1^_3}\). This ordinal has been proven to equal the first uncountable ordinal.
dcterms:subject	Transfinite ordinals Chess Unsolved problems
dbkwik:googology/p...iPageUsesTemplate	dbkwik:resource/IC0Df_d8btr2qfAcMww5xQ== dbkwik:resource/4Yinzn8rermcG1agWBAwNw== dbkwik:resource/yT3JrwLDjx1EXiHBG5CO8g== dbkwik:resource/eWw3cZ_R68BPy4BHDgxCkQ==
abstract	There are a few variants of this ordinal: * If an infinite number of pieces are allowed, the supremum is called \(\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}}\). * With 3D chess, the supremum is called \(\omega_1^{\mathfrak{Ch}_3}\). * With 3D chess with an infinite number of pieces, the supremum is called \(\omega_1^_3}\). This ordinal has been proven to equal the first uncountable ordinal. Evans and Hamkins proved that \(\omega_1^\mathfrak{Ch}\) and \(\omega_1^{\mathfrak{Ch}_3}\) are at most the Church-Kleene ordinal, and \(\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}} \leq \omega_1\). Although it has not been proven, it is believed that all these ordinals are as large as possible — that is, \(\omega_1^\mathfrak{Ch} = \omega_1^{\mathfrak{Ch}_3} = \omega_1^ ext{CK}\) and \(\omega_1^{\mathfrak{Ch}_{\!\!\!\!\sim}} = \omega_1\).

OpenLink Virtuoso version 07.20.3217, on Linux (x86_64-pc-linux-gnu), Standard Edition
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2012 OpenLink Software