Selection over classes of ordinals expanded by monadic predicates
TLDR
A criterion for a class C of ordinals to have the property that every monadic formula φ has a selector over it is introduced and the existence of S ⊆ ω ω is deduced.About:
This article is published in Annals of Pure and Applied Logic.The article was published on 2010-05-01 and is currently open access. It has received 7 citations till now. The article focuses on the topics: Monadic predicate calculus.read more
Citations
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Posted Content
Uniformization and Skolem functions in the class of trees
Shmuel Lifsches,Saharon Shelah +1 more
TL;DR: This work defines a subclass of the class of tame trees (trees with a definable choice function) and proves that this is exactly the class (actually set) of trees with definable Skolem functions.
Journal Article
Review: S. Feferman, R. L. Vaught, The First Order Properties of Products of Algebraic Systems
Journal ArticleDOI
Selection in the monadic theory of a countable ordinal
TL;DR: It is shown that for every ordinal α ≥ ωω there are formulas having no selector in the structure (α, <), and a partial extension of the Büchi-Landweber solvability theorem to all countable ordinals is state.
Book ChapterDOI
Selection and uniformization problems in the monadic theory of ordinals: a survey
TL;DR: This paper surveys some fundamental algorithmic questions and recent results regarding selection and uniformization and presents a natural generalization of the Church problem to ordinals when some additional requirements are imposed on the uniformizing formula ψ(X, Y).
Journal ArticleDOI
Regular sets over extended tree structures
TL;DR: The well-known equivalence between languages recognized by finite automata, sets of vertices MSO definable in a tree-structure and sets of pushdown contexts generated by pushdown-automata is extended to k-iterated pushdown automata.
References
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Book ChapterDOI
Solving sequential conditions by finite-state strategies
TL;DR: In this article, the authors present an algorithm which decides whether or not a condition X, Y stated in sequential calculus admits a finite automata solution, and produces one if it exists.
Journal ArticleDOI
The first order properties of products of algebraic systems
Solomon Feferman,R. L. Vaught +1 more
Journal ArticleDOI
The monadic theory of order
TL;DR: It is proved that the monadic theory of the real order is undecidable, which means that all known results in a unified way are proved.
Book ChapterDOI
Monadic Second-Order Theories
TL;DR: In this paper, the authors make a case for monadic second-order logic as a good source of theories that are both expressive and manageable, and illustrate two powerful decidability techniques here.
Related Papers (5)
The Monadic Theory of Morphic Infinite Words and Generalizations
Olivier Carton,Wolfgang Thomas +1 more