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e mondi formul @Y A is selector for formul '@Y A in struture w if there exists unique suset P of w whih stises nd this P lso stises 'F e show tht for every ordinl ! ! ! there re formuls hving no seletor in the struture @; <AF por !1D we deide whih formuls hve seletor in @; <AD nd onstrut seletors for themF e dedue the… (More)

Dedicated with deepest appreciation and respect to Boris Abramovich Trakhtenbrot whose inspiration as a teacher, a researcher and a role model has been guiding us and many others for many years. Abstract. A formula ψ(Y) is a selector for a formula ϕ(Y) in a structure M if there exists a unique Y that satisfies ψ in M and this Y also satisfies ϕ. A formula… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t A monadic formula ψ(Y) is a selector for a monadic formula ϕ(Y) in a… (More)

A monadic formula ψ(Y) is a selector for a monadic formula ϕ(Y) in a structure M if ψ defines in M a unique subset P of the domain and this P also satisfies ϕ in M. If C is a class of structures and ϕ is a selector for ψ in every M ∈ C, we say ϕ is a selector for ϕ over C. For a monadic formula ϕ(X, Y) and ordinals α ≤ ω 1 and δ < ω ω , we decide whether… (More)

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