Mathematical Logic Fall 2004 Professor R. Moosa Contents
... Definition 2.5. Var = {v0 , v1 , v2 , . . .} is a countably infinite set of symbols whose elements are called variables. We assume that vm 6= vn for m 6= n and we assume that no variable appears as a function or relation symbol in any language that we will ever consider. Remark. We often use x, y, z ...
... Definition 2.5. Var = {v0 , v1 , v2 , . . .} is a countably infinite set of symbols whose elements are called variables. We assume that vm 6= vn for m 6= n and we assume that no variable appears as a function or relation symbol in any language that we will ever consider. Remark. We often use x, y, z ...
When Bi-Interpretability Implies Synonymy
... b. U ` a,b∈S ∀xa , y b c∈S ∃z c d∈S ∀ud (ud ∈dc z c ↔ (ud ∈da xa ∨ ud =da y b )). Here ‘=da ’ is not really in the language if d 6= a. In this case we read ud =da y b simply as ⊥. It’s a nice exercise to show that e.g. ACA0 and GB are sequential. Closely related to AS is adjunctive class theory ac. ...
... b. U ` a,b∈S ∀xa , y b c∈S ∃z c d∈S ∀ud (ud ∈dc z c ↔ (ud ∈da xa ∨ ud =da y b )). Here ‘=da ’ is not really in the language if d 6= a. In this case we read ud =da y b simply as ⊥. It’s a nice exercise to show that e.g. ACA0 and GB are sequential. Closely related to AS is adjunctive class theory ac. ...
santhanam_ratlocc2011
... • PRGs exist non-constructively for any natural class of properties (by the probabilistic method), but when do quick PRGs exist? • Theorem [NW, IW, KvM] : There is a quick PRG against SIZEA(poly) iff there are explicit functions which are hard against A-oracle circuits of size 2o(n) ...
... • PRGs exist non-constructively for any natural class of properties (by the probabilistic method), but when do quick PRGs exist? • Theorem [NW, IW, KvM] : There is a quick PRG against SIZEA(poly) iff there are explicit functions which are hard against A-oracle circuits of size 2o(n) ...
