ERDOS-SZEKERES-TYPE STATEMENTS: RAMSEY FUNCTION AND DECIDABILITY IN DIMENSION 1

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286480" target="_blank" >RIV/00216208:11320/14:10286480 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1215/00127094-2785915" target="_blank" >http://dx.doi.org/10.1215/00127094-2785915</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1215/00127094-2785915" target="_blank" >10.1215/00127094-2785915</a>

Result language
angličtina
Original language name
ERDOS-SZEKERES-TYPE STATEMENTS: RAMSEY FUNCTION AND DECIDABILITY IN DIMENSION 1
Original language description
A classical and widely used lemma of Erdos and Szekeres asserts that for every n there exists N such that every N-term sequence a of real numbers contains an n-term increasing subsequence or an n-term nonincreasing subsequence; quantitatively, the smallest N with this property equals (n - 1)(2) + 1. We express this lemma by saying that the set of predicates Phi = {x(1) < x(2), x(1) > x(2)} is Erdos-Szekeres with Ramsey function ES Phi (n) = (n - 1)(2) + 1. In general, we consider an arbitrary finite setPhi = {Phi(1), ... , Phi(m)} of semialgebraic predicates, meaning that each Phi(j) = Phi(j) (x(1), ... , x(k)) is a Boolean combination of polynomial equations and inequalities in some number k of real variables. We define Phi to be Erdos-Szekeres if for every n there exists N such that each N-term sequence (a) of real numbers has an n-term subsequence (b) such that at least one of the Phi(j) holds everywhere on (b) which means that Phi(j) (b(i1), ... , b(ik)) holds for every choice of
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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