scholarly journals Uniformization, choice functions and well orders in the class of trees

1996 ◽  
Vol 61 (4) ◽  
pp. 1206-1227 ◽  
Author(s):  
Shmuel Lifsches ◽  
Saharon Shelah
Keyword(s):  
Choice Function ◽  
Order Theory ◽  
Second Order ◽  
Close Connection ◽  
Choice Functions

AbstractThe 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 first class don't have a definable choice function and the trees in the second class have even a definable well ordering of their elements. This has a close connection to the uniformization problem.

Uniformization and skolem functions in the class of trees

1998 ◽  
Vol 63 (1) ◽  
pp. 103-127 ◽  
Author(s):  
Shmuel Lifsches ◽  
Saharon Shelah
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Choice Functions ◽  
Skolem Functions ◽  
The Way

AbstractThe 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 [6] where the question was asked only with respect to choice functions. A natural subclass is defined and proved to be the class of trees with definable Skolem functions. Along the way we investigate the spectrum of definable well orderings of well ordered chains.

scholarly journals Choice functions and well-orderings over the infinite binary tree

2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Arnaud Carayol ◽  
Christof Löding ◽  
Damian Niwinski ◽  
Igor Walukiewicz
Keyword(s):  
Binary Tree ◽  
Choice Function ◽  
Second Order ◽  
Order Logic ◽  
Automata Theory ◽  
Choice Functions ◽  
Infinite Trees ◽  
Second Order Logic ◽  
Inherent Ambiguity ◽  
Monadic Second Order Logic

AbstractWe give a new proof showing that it is not possible to define in monadic second-order logic (MSO) a choice function on the infinite binary tree. This result was first obtained by Gurevich and Shelah using set theoretical arguments. Our proof is much simpler and only uses basic tools from automata theory. We show how the result can be used to prove the inherent ambiguity of languages of infinite trees. In a second part we strengthen the result of the non-existence of an MSO-definable well-founded order on the infinite binary tree by showing that every infinite binary tree with a well-founded order has an undecidable MSO-theory.

scholarly journals Surface wavepackets subject to an abrupt depth change. Part 1. Second-order theory

2021 ◽  
Vol 915 ◽  
Author(s):  
Yan Li ◽  
Yaokun Zheng ◽  
Zhiliang Lin ◽  
Thomas A.A. Adcock ◽  
Ton S. van den Bremer
Keyword(s):  
Order Theory ◽  
Second Order

Abstract

A Comment on Arrow’s Impossibility Theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alec Sandroni ◽  
Alvaro Sandroni
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Preference ◽  
Social Choice Function ◽  
Individual Preference ◽  
Impossibility Theorem ◽  
Preference Order ◽  
Individual Choice ◽  
Choice Functions ◽  
Preference Orders

AbstractArrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

Invariant relative orbits for satellite constellations: A second order theory

2006 ◽  
Vol 181 (1) ◽  
pp. 6-20 ◽  
Author(s):  
F.A. Abd El-Salam ◽  
I.A. El-Tohamy ◽  
M.K. Ahmed ◽  
W.A. Rahoma ◽  
M.A. Rassem
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Satellite Constellations

How Second-Order Is the Regional Level? An Analysis of Tweets in Simultaneous Campaigns

2017 ◽  
Vol 65 (4) ◽  
pp. 1021-1039
Author(s):  
Nicolas Bouteca ◽  
Evelien D’heer ◽  
Steven Lannoo
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Regional Level ◽  
The Political ◽  
Voting Behaviour ◽  
National Parliament ◽  
Political Experience ◽  
Regional Elections

This article puts the second-order theory for regional elections to the test. Not by analysing voting behaviour but with the use of campaign data. The assumption that regional campaigns are overshadowed by national issues was verified by analysing the campaign tweets of Flemish politicians who ran for the regional or national parliament in the simultaneous elections of 2014. No proof was found for a hierarchy of electoral levels but politicians clearly mix up both levels in their tweets when elections coincide. The extent to which candidates mix up governmental levels can be explained by the incumbency past of the candidates, their regionalist ideology, and the political experience of the candidates.

A second-order theory for resonance capture in corotation centers

1999 ◽  
Vol 47 (5) ◽  
pp. 643-652 ◽  
Author(s):  
C. Beauge ◽  
A. Lemaı̂tre ◽  
S. Jancart
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Resonance Capture
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