Monadic second order definable relations on the binary tree

1987 ◽  
Vol 52 (1) ◽  
pp. 219-226 ◽  
Author(s):  
Hans Läuchli ◽  
Christian Savioz
Keyword(s):  
Binary Tree ◽  
Order Theory ◽  
Second Order ◽  
Simple Characterization ◽  
Free Variables ◽  
Power Set ◽  
Definable Relations ◽  
Individual Variables

AbstractLet S2S [WS2S] respectively be the strong [weak] monadic second order theory of the binary tree T in the language of two successor functions. An S2S-formula whose free variables are just individual variables defines a relation on T (rather than on the power set of T). We show that S2S and WS2S define the same relations on T, and we give a simple characterization of these relations.

Models of Second-Order Zermelo Set Theory

1999 ◽  
Vol 5 (3) ◽  
pp. 289-302 ◽  
Author(s):  
Gabriel Uzquiano
Keyword(s):  
Set Theory ◽  
Order Theory ◽  
Second Order ◽  
First Order Theory ◽  
Set Relation ◽  
Remarkable Result ◽  
Definition Of ◽  
Skolem Theorem ◽  
Ernst Zermelo

In [12], Ernst Zermelo described a succession of models for the axioms of set theory as initial segments of a cumulative hierarchy of levels UαVα. The recursive definition of the Vα's is:Thus, a little reflection on the axioms of Zermelo-Fraenkel set theory (ZF) shows that Vω, the first transfinite level of the hierarchy, is a model of all the axioms of ZF with the exception of the axiom of infinity. And, in general, one finds that if κ is a strongly inaccessible ordinal, then Vκ is a model of all of the axioms of ZF. (For all these models, we take ∈ to be the standard element-set relation restricted to the members of the domain.) Doubtless, when cast as a first-order theory, ZF does not characterize the structures 〈Vκ,∈∩(Vκ×Vκ)〉 for κ a strongly inaccessible ordinal, by the Löwenheim-Skolem theorem. Still, one of the main achievements of [12] consisted in establishing that a characterization of these models can be attained when one ventures into second-order logic. For let second-order ZF be, as usual, the theory that results from ZF when the axiom schema of replacement is replaced by its second-order universal closure. Then, it is a remarkable result due to Zermelo that second-order ZF can only be satisfied in models of the form 〈Vκ,∈∩(Vκ×Vκ)〉 for κ a strongly inaccessible ordinal.

scholarly journals Definability in the monadic second-order theory of successor

1969 ◽  
Vol 34 (2) ◽  
pp. 166-170 ◽  
Author(s):  
J. Richard Buchi ◽  
Lawrence H. Landweber
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Predicate Calculus ◽  
Relational System ◽  
First Order ◽  
Individual Variables ◽  
Order Predicate Calculus

Let be a relational system whereby D is a nonempty set and P1 is an m1-ary relation on D. With we associate the (weak) monadic second-order theory consisting of the first-order predicate calculus with individual variables ranging over D; monadic predicate variables ranging over (finite) subsets of D; monadic predicate quantifiers; and constants corresponding to P1, P2, …. We will often use ambiguously to mean also the set of true sentences of .

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

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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