TY - JOUR

T1 - Selection over classes of ordinals expanded by monadic predicates

AU - Rabinovich, Alexander

AU - Shomrat Amit, A.

PY - 2010/5

Y1 - 2010/5

N2 - A monadic formula ψ(Y) is a selector for a monadic formula (Y) in a structure M if ψ defines in M a unique subset P of the domain and this P also satisfies in M. If C is a class of structures and is a selector for ψ in every MC, we say that is a selector for over C.For a monadic formula (X,Y) and ordinals α≤ω1 and .δ <ωω, we decide whether there exists a monadic formula ψ(X,Y) such that for every P ⊆ α of order-type smaller than .δ , ψ(P,Y) selects (P,Y) in (α,<). If so, we construct such a ψ. We introduce a criterion for a class C of ordinals to have the property that every monadic formula has a selector over it. We deduce the existence of S ⊆ ωω such that in the structure (ωω,<,S) every formula has a selector.Given a monadic sentence π and a monadic formula (Y), we decide whether has a selector over the class of countable ordinals satisfying π, and if so, construct one for it.

AB - A monadic formula ψ(Y) is a selector for a monadic formula (Y) in a structure M if ψ defines in M a unique subset P of the domain and this P also satisfies in M. If C is a class of structures and is a selector for ψ in every MC, we say that is a selector for over C.For a monadic formula (X,Y) and ordinals α≤ω1 and .δ <ωω, we decide whether there exists a monadic formula ψ(X,Y) such that for every P ⊆ α of order-type smaller than .δ , ψ(P,Y) selects (P,Y) in (α,<). If so, we construct such a ψ. We introduce a criterion for a class C of ordinals to have the property that every monadic formula has a selector over it. We deduce the existence of S ⊆ ωω such that in the structure (ωω,<,S) every formula has a selector.Given a monadic sentence π and a monadic formula (Y), we decide whether has a selector over the class of countable ordinals satisfying π, and if so, construct one for it.

KW - Decidability

KW - Monadic logic of order

KW - Selection problem

KW - Uniformization problem

UR - http://www.scopus.com/inward/record.url?scp=77952291519&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2009.12.004

DO - 10.1016/j.apal.2009.12.004

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AN - SCOPUS:77952291519

SN - 0168-0072

VL - 161

SP - 1006

EP - 1023

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 8

ER -