Again from wiki. This vis-a-vis R. Dale's point about possible sources, if any, for Carnap's lucidity in "Aufbau", which indeed predates Tarksi by a number of years.
"The existential and universal "operators": PM adds " (x) " to represent the contemporary symbolism " for all x " i.e. " ∀x ", and it uses a backwards serifed E to represent " there exists an x " i.e. " (Ǝx) ", i.e. the contemporary ∃x. The typical notation would be similar to the following:
" (x) ▪ φx " means " for all values of variable x, function φ evaluates to true
" (Ǝx) ▪ φx means " for all values of variable x, function φ evaluates to true."
All dogs are owned by the man.
The man owns a dog.
--- etc.
Cfr. Carnap, "Homo habet canem"
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