# A lower bound on Gowers' FIN_k theorem

@article{Kreuzer2015ALB, title={A lower bound on Gowers' FIN\_k theorem}, author={Alexander P. Kreuzer}, journal={arXiv: Logic}, year={2015} }

Gowers' FIN$_k$ theorem, also called Gowers' pigeonhole principle or Gowers' theorem, is a Ramsey-type theorem. It first occurred in the study of Banach space theory and is a natural generalization of Hindman's theorem. In this short note, we will show that Gowers' FIN$_k$ theorem does not follow from ACA$_0$.

#### References

SHOWING 1-8 OF 8 REFERENCES

Hindman's theorem, ultrafilters, and reverse mathematics

- Mathematics, Computer Science
- Journal of Symbolic Logic
- 2004

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 The theorem. Expand

A Simple Proof and Some Difficult Examples for Hindman's Theorem

- Mathematics, Computer Science
- Notre Dame J. Formal Log.
- 2012

We give a short, explicit proof of Hindman's Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. We give several exampls of… Expand

Finite Sums from Sequences Within Cells of a Partition of N

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 1974

The principal result of this paper establishes the validity of a conjecture that, if the natural numbers are divided into two classes, then there is a sequence drawn from one of those classes such that all finite sums of distinct members of that sequence remain in the same class. Expand

Lipschitz functions on classical spaces

- Computer Science, Mathematics
- Eur. J. Comb.
- 1992

Abstract We show that, for everyɛ > 0 and every Lipschitz functionf from the unit sphere of the Banach spacec0 to ℝ, there is an infinite-dimensional subspace ofc0, on the unit sphere of whichf… Expand

Subsystems of second order arithmetic

- Mathematics, Computer Science
- Perspectives in mathematical logic
- 1999

The results show clear trends in the development of mathematics within Subsystems of Z2 and in particular in the areas of arithmetical comprehension and models of Sub system design. Expand

Open Questions in Reverse Mathematics

- Computer Science
- The Bulletin of Symbolic Logic
- 2011

Abstract We present a list of open questions in reverse mathematics, including some relevant background information for each question. We also mention some of the areas of reverse mathematics that… Expand