scholarly journals New bounds on the strength of some restrictions of Hindman’s Theorem

Computability ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 139-153
Author(s):  
Lorenzo Carlucci ◽  
Leszek Aleksander Kołodziejczyk ◽  
Francesco Lepore ◽  
Konrad Zdanowski
Keyword(s):  
Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 253-263 ◽  
Author(s):  
Barbara F. Csima ◽  
Damir D. Dzhafarov ◽  
Denis R. Hirschfeldt ◽  
Carl G. Jockusch, Jr. ◽  
Reed Solomon ◽  
...  

2019 ◽  
Vol 62 (3) ◽  
pp. 577-581
Author(s):  
Justin Tatch Moore

AbstractFree binary systems are shown not to admit idempotent means. This refutes a conjecture of the author. It is also shown that the extension of Hindman’s theorem to nonassociative binary systems formulated and conjectured by the author is false.


2004 ◽  
Vol 69 (1) ◽  
pp. 65-72 ◽  
Author(s):  
Jeffry L. Hirst

AbstractAssuming CH. Hindman [2] showed that the existence of certain ultrafilters on the power set of the natural numbers is equivalent to Hindman's Theorem. Adapting this work to a countable setting formalized in RCA0, this article proves the equivalence of the existence of certain ultrafilters on countable Boolean algebras and an iterated form of Hindman's Theorem, which is closely related to Milliken's Theorem. A computable restriction of Hindman's Theorem follows as a corollary.


2003 ◽  
Vol 53 (2) ◽  
pp. 319-342
Author(s):  
Richard N. Ball ◽  
James N. Hagler
Keyword(s):  

1978 ◽  
Vol 25 (2) ◽  
pp. 174-180 ◽  
Author(s):  
Keith R. Milliken
Keyword(s):  

2011 ◽  
Vol 76 (1) ◽  
pp. 353-360 ◽  
Author(s):  
Henry Towsner

AbstractHindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.


2018 ◽  
Vol 97 (3) ◽  
pp. 471-477
Author(s):  
Uri Andrews ◽  
Isaac Goldbring
Keyword(s):  

2016 ◽  
Vol 16 (02) ◽  
pp. 1650005 ◽  
Author(s):  
Wen Chean Teh

Hindman’s theorem says that every finite coloring of the natural numbers has a monochromatic set of finite sums. Ramsey algebras are structures that satisfy an analogue of Hindman’s Theorem. This paper introduces Ramsey algebras and presents some elementary results. Furthermore, their connection to Ramsey spaces will be addressed.


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