Amit Shomrat

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A monadic formula (Y ) is a selector for a formula '(Y ) in a structure M if there exists a unique subset P of M which satis es and this P also satis es '. We show that for every ordinal ! there are formulas having no selector in the structure ( ;<). For !1, we decide which formulas have a selector in ( ;<), and construct selectors for them. We deduce the(More)
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 ψ(X,Y ) uniformizes a formula φ(X, Y ) in a structure M if for every X there exists a unique Y such that ψ(X,Y ) holds in M and for this Y , φ(X,Y ) also holds in M. In this paper we survey some(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 ≤ ω1 and δ < ω, we decide whether there(More)
A monadic formula ψ(Y ) is a selector for a monadic formula φ(Y ) in a structure M if ψ defines inM a unique subset P of the domain and this P also satisfies φ inM. If C is a class of structures and φ is a selector for ψ in everyM ∈ C, we say that φ is a selector for φ over C. For a monadic formula φ(X, Y ) and ordinals α ≤ ω1 and δ < ω , we decide whether(More)
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