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- W2483226204 abstract "As the axiom of choice implies, for every relation (Rsubseteq Xtimes Y) there exists a graph of a total function (f:pi _X(R) rightarrow Y) that is contained in R (such a graph is called a uniformization of R). A natural question asks in which cases such a function f is definable. A particular instance of this problem is, when R is an mso-definable set of pairs of trees and we ask about mso-definable f. This question is known as Rabin’s uniformization question. The negative answer to this question was given by Gurevich and Shelah [GS83] (see [CL07] for a simplified proof). They proved that there is no mso formula (psi (x,X)) that chooses from every non-empty subset X of the complete binary tree a unique element x of X. This result is known as undefinability of a choice function on the complete binary tree. On the other hand, the formula saying that x is the (le )-minimal element of X is a choice formula on (omega )-words. In [Sie75, LS98, Rab07] it is proved that any mso-definable relation on (omega )-words admits an mso-definable uniformization." @default.
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- W2483226204 date "2016-01-01" @default.
- W2483226204 modified "2023-10-06" @default.
- W2483226204 title "Uniformization on Thin Trees" @default.
- W2483226204 doi "https://doi.org/10.1007/978-3-662-52947-8_8" @default.
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