Unterlogiker: ‘In logic, there are morals.’ Überlogiker: ‘Hail Gödelian immoralism!’
Arithmetisation of syntax is usually realised through Gödel-encoding with prime factorisation, but it’s more complicated within PA. Try to think of a way to express ‘the exponent of prime p in factorisation of n is k’ as a predicate with three variables (p,n,k) in PA’s language.
Let K be a number field, S a set of primes w/ all primes above p > 2, T a finitely generated ℤₚ-module w/ continuous Gal(K_S/K)-action, and K_∞/K a ℤₚ-extension w/ Galois group Γ. Since cdₚ(Gal(K_S/K)) = 2, you can use this fact to show H²_iw(K_S/K_∞,T)_Γ ≅ H²(K_S/K,T).
All’em speds broke asf, they can’t cop no AMG Merc, My ho compute Gal(ℚ(∛2, ω)/ℚ) ‘til ha brain hurt, I finish off thih bih then ghost her ‘cause I’m a real jerk, All’em speddy hoes only good for bein’ left in tha dirt, From Spec ℚₚ to Spec ℤₚ, I’m poppin’ that Hodge perc.
Given two posets P and Q, P × Q is treated as the poset with the pointwise order ((a, b) < (c, d) ⇔ a < c ∧ b < d). Okay, now let Tₖ be Fₖ’s closure under finite products (modulo Kenyatta equivalence). Then, for finite k, |Tₖ| is equal to the Catalan number indexed by k + 2.
Ain’t nobody care ‘bout none of yo’ goofy-ass questions, sped.
Dr Kenyatta and I would also like to mention here that for any ℓ-adic local field K, the absolute Galois group of K admits G of the second type as a subgroup, but it can’t admit G of the first type as a subgroup for cohomological dimension reasons. #ÜVL5AlgebraicNT
Can your downstream unterlogiker ass even show that ∀x(Fx ⇔ Gx ∨ Hx), ∃xGx, ∀x(Fx→∀xHx) ⊢ ∀xFx?
We gon’ be slidin’ with them sinister algebraists right there, js watch.
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