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):  
Hindman’S Theorem

scholarly journals The reverse mathematics of Hindman’s Theorem for sums of exactly two elements

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 ◽  
...  
Keyword(s):  
Reverse Mathematics ◽  
Hindman’S Theorem

Nonexistence of Idempotent Means on Free Binary Systems

2019 ◽  
Vol 62 (3) ◽  
pp. 577-581
Author(s):  
Justin Tatch Moore
Keyword(s):  
Binary Systems ◽  
Hindman’S Theorem

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.

Hindman's theorem, ultrafilters, and reverse mathematics

2004 ◽  
Vol 69 (1) ◽  
pp. 65-72 ◽  
Author(s):  
Jeffry L. Hirst
Keyword(s):  
Reverse Mathematics ◽  
Boolean Algebras ◽  
Natural Numbers ◽  
Hindman’S Theorem ◽  
Power Set

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.

scholarly journals Flow Compactifications of Nondiscrete Monoids, Idempotents and Hindman's Theorem

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

scholarly journals Hindman's theorem and groups

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

scholarly journals Hindman's theorem: an ultrafilter argument in second order arithmetic

2011 ◽  
Vol 76 (1) ◽  
pp. 353-360 ◽  
Author(s):  
Henry Towsner
Keyword(s):  
Second Order ◽  
Second Order Arithmetic ◽  
Hindman’S Theorem ◽  
Combinatorial Theorem ◽  
Order Arithmetic

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.

scholarly journals Hindman’s theorem and idempotent types

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

scholarly journals Ramsey algebras

2016 ◽  
Vol 16 (02) ◽  
pp. 1650005 ◽  
Author(s):  
Wen Chean Teh
Keyword(s):  
Natural Numbers ◽  
Hindman’S Theorem ◽  
Finite Sums

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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