Amit Shomrat

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e mon—di™ formul— @Y A is — selector for — formul— '@Y A in — stru™ture w if there exists — unique su˜set P of w whi™h s—tises —nd this P —lso s—tises 'F ‡e show th—t for every ordin—l ! ! ! there —re formul—s h—ving no sele™tor in the stru™ture @; <AF por !1D we de™ide whi™h formul—s h—ve — sele™tor in @; <AD —nd ™onstru™t sele™tors for themF ‡e dedu™e 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)
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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