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Post by P1kachu on Jun 12, 2015 10:16:39 GMT
Omega DEF + 1 ( ͡° ÍÊ Í¡Â°) unlike most of other transfinite ordinals, Omega DEF+anything (even another transfinite) is still Omega DEF( ͡° ͜o ͡°) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 12, 2015 10:17:45 GMT
unlike most of other transfinite ordinals, Omega DEF+anything (even another transfinite) is still Omega DEF( ͡° ͜o ͡°) you lost ( ͡° ͜ʖ ͡°) |
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Post by P1kachu on Jun 12, 2015 10:18:22 GMT
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 12, 2015 10:19:35 GMT
you lost ( ͡° ÍÊ Í¡Â°) ROUND 2: 1. ( ͡° Ío ͡°) âR { { â[Ï], s: R([Ï],t) â ([Ï] = "xáµ¢ â xâ±¼" ⧠t(xáµ¢) â t(xâ±¼)) ⨠([Ï] = "xáµ¢ = xâ±¼" ⧠t(xáµ¢) = t(xâ±¼)) ⨠([Ï] = "(¬θ)" ⧠¬R([θ], t)) ⨠([Ï] = "([θ]â§Î¾)" ⧠R([θ], t) ⧠R([ξ], t)) ⨠([Ï] = "âxáµ¢(θ)" ⧠âtâ²: R([θ], tâ²)) (where tâ² is a copy of t with xáµ¢ changed) } â R([Ï],s) } Call a natural number m "Rayo-namable in n symbols" if there is a formula Ï(x1) with less than n symbols and x1 as its only free variable that satisfies the following properties: There is a variable assignment s, assigning x1:=m, such that Sat([Ï(x1)],s). For any variable assignment t, if Sat([Ï(x1)],t), t must have x1=m. Rayo(n), then, is the smallest number greater than all numbers Rayo-namable in n symbols. My entry is Rayo(10 100) ( ͡° ͜ʖ ͡°) |
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Post by P1kachu on Jun 12, 2015 10:24:15 GMT
ROUND 2: 1. ( ͡° Ío ͡°) âR { { â[Ï], s: R([Ï],t) â ([Ï] = "xáµ¢ â xâ±¼" ⧠t(xáµ¢) â t(xâ±¼)) ⨠([Ï] = "xáµ¢ = xâ±¼" ⧠t(xáµ¢) = t(xâ±¼)) ⨠([Ï] = "(¬θ)" ⧠¬R([θ], t)) ⨠([Ï] = "([θ]â§Î¾)" ⧠R([θ], t) ⧠R([ξ], t)) ⨠([Ï] = "âxáµ¢(θ)" ⧠âtâ²: R([θ], tâ²)) (where tâ² is a copy of t with xáµ¢ changed) } â R([Ï],s) } Call a natural number m "Rayo-namable in n symbols" if there is a formula Ï(x1) with less than n symbols and x1 as its only free variable that satisfies the following properties: There is a variable assignment s, assigning x1:=m, such that Sat([Ï(x1)],s). For any variable assignment t, if Sat([Ï(x1)],t), t must have x1=m. Rayo(n), then, is the smallest number greater than all numbers Rayo-namable in n symbols. My entry is Rayo(10 100) ( ͡° ÍÊ Í¡Â°) Too naive ( ͡° ͜ʖ ͡°) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 12, 2015 10:24:59 GMT
∀R { { ∀[ψ], s: R([ψ],t) ↔ ([ψ] = "xᵢ ∈ xⱼ" ∧ t(xᵢ) ∈ t(xⱼ)) ∨ ([ψ] = "xᵢ = xⱼ" ∧ t(xᵢ) = t(xⱼ)) ∨ ([ψ] = "(¬θ)" ∧ ¬R([θ], t)) ∨ ([ψ] = "([θ]∧ξ)" ∧ R([θ], t) ∧ R([ξ], t)) ∨ ([ψ] = "∃xᵢ(θ)" ∧ ∃t′: R([θ], t′)) (where t′ is a copy of t with xᵢ changed) } ⇒ R([ϕ],s) } Call a natural number m "Rayo-namable in n symbols" if there is a formula ϕ(x1) with less than n symbols and x1 as its only free variable that satisfies the following properties: There is a variable assignment s, assigning x1:=m, such that Sat([ϕ(x1)],s). For any variable assignment t, if Sat([ϕ(x1)],t), t must have x1=m. Rayo(n), then, is the smallest number greater than all numbers Rayo-namable in n symbols. My entry is Rayo(10 100) ( ͡° ͜ʖ ͡°) Too naive ( ͡° ͜ʖ ͡°) u wot ( ͡° ͜ʖ ͡°) |
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Post by P1kachu on Jun 12, 2015 10:38:21 GMT
Too naive ( ͡° ÍÊ Í¡Â°) u wot ( ͡° ÍÊ Í¡Â°) its a naive extensil ( ͡° ͜ʖ ͡°) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 12, 2015 10:39:22 GMT
its a naive extensil ( ͡° ͜ʖ ͡°) of what? ( ͡° ͜ʖ ͡°) |
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Post by P1kachu on Jun 12, 2015 10:48:21 GMT
its a naive extensil ( ͡° ͜ʖ ͡°) of what? ( ͡° ͜ʖ ͡°) The 10 100 of Rayo(10 100) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 12, 2015 10:51:22 GMT
not a naive extension, that would mean that I took an existing number and increase without changing its definition Rayo Rayo(10100)(10 100) was not a naive extension until Rayo(10 100) has been defined |
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Post by P1kachu on Jun 12, 2015 11:02:58 GMT
not a naive extension, that would mean that I took an existing number and increase without changing its definition Rayo Rayo(10100)(10 100) was not a naive extension until Rayo(10 100) has been defined Rayo RayoRayoRayoRayoRayoRayoRayoRayoRayoRayo(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10 100) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 12, 2015 14:15:15 GMT
not a naive extension, that would mean that I took an existing number and increase without changing its definition Rayo Rayo(10100)(10 100) was not a naive extension until Rayo(10 100) has been defined Rayo RayoRayoRayoRayoRayoRayoRayoRayoRayoRayo(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10 100) now that smaller numbers using Rayo(n) has been defined, that IS a naive extension |
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Post by P1kachu on Jun 13, 2015 0:11:41 GMT
Rayo RayoRayoRayoRayoRayoRayoRayoRayoRayoRayo(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10100)(10 100) now that smaller numbers using Rayo(n) has been defined, that IS a naive extension I don't understand ( ͡° ͜ʖ ͡°) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jun 13, 2015 9:51:00 GMT
now that smaller numbers using Rayo(n) has been defined, that IS a naive extension I don't understand ( ͡° ͜ʖ ͡°) 2bad4u ( ͡° ͜ʖ ͡°) |
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Post by P1kachu on Jun 13, 2015 10:45:03 GMT
I don't understand ( ͡° ͜ʖ ͡°) 2bad4u ( ͡° ͜ʖ ͡°) 42bad69me ( ͡° ͜ʖ ͡°) |
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