Simon Thomas
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Registered User
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Academically, I am the great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-grandchild of Isaac Newton.
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May 16 |
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Are the two meanings of “undecidable” related? Better to be a platonist ... |
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May 16 |
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Are the two meanings of “undecidable” related? @ Joel: your disagreement with Noah seems to based on whether you use extensional or intensional definitions of sets of natural numbers. Your example clearly uses an intensional definition and could be simplified as follows: Let X be an undecidable set of natural numbers and let Y be a decidable set of natural numbers. Let Z be X if ZFC is consistent and Y if ZFC is inconsistent. Then the decidability of Z is independent of ZFC. |
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Mar 30 |
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Interpretability and consistency strength This is not true in general since it would imply that any two consistent theories were mutually interpretable. However, the complete theory of the field of real numbers cannot be interpreted in the complete theory of the complex field. |
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Mar 17 |
awarded | ● Yearling |
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Jan 24 |
awarded | ● Favorite Question |
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Jan 23 |
awarded | ● Enlightened |
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Jan 23 |
awarded | ● Nice Answer |
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Dec 25 |
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Suzuki group order @Jim: Rutgers doesn't have it online either. My guess/memory is that it also treats the Suzuki and Ree groups as the corresponding result for these groups is also needed for the main application: the classification of the simple periodic linear groups. In any case, these cases were done earlier by Kegal and Stingl. |
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Dec 25 |
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Suzuki group order @Jim: Assuming the Suzuki groups are "sufficiently large", any inclusion is natural. In fact, this is true for any (possibly twisted) Lie type. For example, see: MR0734665 (85k:20094) Reviewed Hartley, B.(4-MANC); Shute, G.(1-WIP) Monomorphisms and direct limits of finite groups of Lie type. Quart. J. Math. Oxford Ser. (2) 35 (1984), no. 137, 49–71. |
