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Oct 2, 2011 at 17:46 comment added Garabed Gulbenkian Thanks alot for your answers and suggestions. I think the main problem here is that the largest "large cardinal numbers" are elements of S because S contains a sub-collection ordinally similar to the class of all ordinal numbers. The theory of S has been much developed since Conway published "On Numbers and Games". Perhaps the theory of S can be formalized in Morse-Kelley set theory but only if that set theory allows the existence of continuously ordered collections containing dense sub-collections which are proper classes.
Sep 30, 2011 at 10:46 history edited Todd Trimble CC BY-SA 3.0
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Sep 29, 2011 at 20:49 history answered Todd Trimble CC BY-SA 3.0