scholarly journals Ramsey theory without pigeonhole principle and the adversarial Ramsey principle

2020 ◽  
Vol 373 (7) ◽  
pp. 5025-5056
Author(s):  
N. de Rancourt
Keyword(s):  
Ramsey Theory ◽  
Pigeonhole Principle

Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns
Keyword(s):  
Harmonic Analysis ◽  
Set Theory ◽  
Harmonic Functions ◽  
Maximal Functions ◽  
Pigeonhole Principle ◽  
Cardinal Invariants ◽  
Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

scholarly journals Recent results in partition (Ramsey) theory for finite lattices

1981 ◽  
Vol 35 (1-3) ◽  
pp. 185-198 ◽  
Author(s):  
Hans Jürgen Prömel ◽  
Bernd Voigt
Keyword(s):  
Ramsey Theory ◽  
Finite Lattices

scholarly journals Abstract topological Ramsey theory for nets

2016 ◽  
Vol 201 ◽  
pp. 314-329 ◽  
Author(s):  
Vassiliki Farmaki ◽  
Dimitris Karageorgos ◽  
Andreas Koutsogiannis ◽  
Andreas Mitropoulos
Keyword(s):  
Ramsey Theory

scholarly journals FRAGMENTS OF APPROXIMATE COUNTING

2014 ◽  
Vol 79 (2) ◽  
pp. 496-525 ◽  
Author(s):  
SAMUEL R. BUSS ◽  
LESZEK ALEKSANDER KOŁODZIEJCZYK ◽  
NEIL THAPEN
Keyword(s):  
Polynomial Time ◽  
Open Problem ◽  
Bounded Arithmetic ◽  
Pigeonhole Principle ◽  
Approximate Counting ◽  
Image Position

AbstractWe study the long-standing open problem of giving $\forall {\rm{\Sigma }}_1^b$ separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek’s theories for approximate counting and their subtheories. We show that the $\forall {\rm{\Sigma }}_1^b$ Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole principle for FPNP functions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of $T_2^1$ augmented with the surjective weak pigeonhole principle for polynomial time functions.

Fundamentals of Ramsey Theory

2021 ◽  
Author(s):  
Aaron Robertson
Keyword(s):  
Ramsey Theory
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