Uniformization and Skolem Functions in the Class of Trees
نویسندگان
چکیده
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have definable Skolem functions (by a monadic formula with parameters)? This continues [LiSh539] where the question was asked only with respect to choice functions. Here we define a subclass of the class of tame trees (trees with a definable choice function) and prove that this is exactly the class (actually set) of trees with definable Skolem functions.
منابع مشابه
Uniformization, Choice Functions and Well Orders in the Class of Trees
Uniformization, choice functions and well orders in the class of trees. ABSTRACT The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with parameters)? A natural dichotomy arises where the trees that fall in the fir...
متن کاملJensen's Sigma* Theory and the Combinatorial Content of V=L
An awkward feature of the fine structure theory of the J α 's is that special parameters are required to make good sense of the notion of " Σ n Skolem hull " for n > 1. The source of the problem is that parameters are needed to uniform Σ n relations when n > 1. The purpose of this article is to indicate how a reformulation of Jensen's Σ * theory (developed for the study of core models) can be u...
متن کاملProofs in Higher-Order Logic
Expansion trees are defined as generalizations of Herbrand instances for formulas in a nonextensional form of higher-order logic based on Church's simple theory of types. Such expansion trees can be defined with or without the use of skolem functions. These trees store substitution terms and either critical variables or skolem terms used to instantiate quantifiers in the original formula and th...
متن کاملeq PROOFS IN HIGHER - ORDER LOGIC
Expansion trees are defined as generalizations of Herbrand instances for formulas in a nonextensional form of higher-order logic based on Church’s simple theory of types. Such expansion trees can be defined with or without the use of skolem functions. These trees store substitution terms and either critical variables or skolem terms used to instantiate quantifiers in the original formula and th...
متن کاملSkolem Odd Difference Mean Graphs
In this paper we define a new labeling called skolem odd difference mean labeling and investigate skolem odd difference meanness of some standard graphs. Let G = (V,E) be a graph with p vertices and q edges. G is said be skolem odd difference mean if there exists a function f : V (G) → {0, 1, 2, 3, . . . , p + 3q − 3} satisfying f is 1−1 and the induced map f : E(G) → {1, 3, 5, . . . , 2q−1} de...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Symb. Log.
دوره 63 شماره
صفحات -
تاریخ انتشار 1998