TY - GEN

T1 - Selection and uniformization problems in the monadic theory of ordinals

T2 - A survey

AU - Rabinovich, Alexander

AU - Shomrat, Amit

PY - 2008

Y1 - 2008

N2 - A formula ψ(Y) is a selector for a formula φ(Y) in a structure if there exists a unique Y that satisfies ψ in and this Y also satisfies φ. A formula ψ(X,Y) uniformizes a formula φ(X,Y) in a structure if for every X there exists a unique Y such that ψ(X,Y) holds in and for this Y, φ(X,Y) also holds in . In this paper we survey some fundamental algorithmic questions and recent results regarding selection and uniformization, when the formulas ψ and φ are formulas of the monadic logic of order and the structure is an ordinal α equipped with its natural order. A natural generalization of the Church problem to ordinals is obtained when some additional requirements are imposed on the uniformizing formula ψ(X,Y). We present what is known regarding this generalization of Church's problem.

AB - A formula ψ(Y) is a selector for a formula φ(Y) in a structure if there exists a unique Y that satisfies ψ in and this Y also satisfies φ. A formula ψ(X,Y) uniformizes a formula φ(X,Y) in a structure if for every X there exists a unique Y such that ψ(X,Y) holds in and for this Y, φ(X,Y) also holds in . In this paper we survey some fundamental algorithmic questions and recent results regarding selection and uniformization, when the formulas ψ and φ are formulas of the monadic logic of order and the structure is an ordinal α equipped with its natural order. A natural generalization of the Church problem to ordinals is obtained when some additional requirements are imposed on the uniformizing formula ψ(X,Y). We present what is known regarding this generalization of Church's problem.

UR - http://www.scopus.com/inward/record.url?scp=49949085604&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-78127-1_31

DO - 10.1007/978-3-540-78127-1_31

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AN - SCOPUS:49949085604

SN - 3540781269

SN - 9783540781264

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 571

EP - 588

BT - Pillars of Computer Science - Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday

A2 - Avron, Arnon

A2 - Dershowitz, Nachum

A2 - Rabinovich, Alexander

ER -