Abstract
A simple geometric assertion of Ramsey type, concerning families of straight lines in the Euclidean space
Funding source: Shota Rustaveli National Science Foundation
Award Identifier / Grant number: FR-18-6190
Funding statement: This work was partially supported by Shota Rustaveli National Science Foundation of Georgia, Grant FR-18-6190.
References
[1] P. Erdös and G. Szekeres, A combinatorial problem in geometry, Compos. Math. 2 (1935), 463–470. 10.1007/978-0-8176-4842-8_3Search in Google Scholar
[2] R. L. Graham, B. L. Rothschild and J. H. Spencer, Ramsey Theory, 2ond ed., Wiley Intersci. Ser. Discrete Math. Optim., John Wiley & Sons, New York, 1990. Search in Google Scholar
[3] T. J. Jech, Set Theory, Springer Monogr. Math., Springer, Berlin, 2003. Search in Google Scholar
[4] M. Katz and J. Reimann, An Introduction to Ramsey Theory. Fast Functions, Infinity, and Metamathematics, Stud. Math. Libr. 87, American Mathematical Society, Providence, 2018. 10.1090/stml/087Search in Google Scholar
[5] A. Kharazishvili, Some geometric consequences of Ramsey’s combinatorial theorem, Bull. TICMI 16 (2012), no. 1, 34–42. Search in Google Scholar
[6] P. Komjáth and V. Totik, Problems and Theorems in Classical Set Theory, Probl. Books in Math., Springer, New York, 2006. Search in Google Scholar
[7] F. P. Ramsey, On a problem of formal logic, Proc. Lond. Math. Soc. 2 (1930), no. 1, 264–286. 10.1007/978-0-8176-4842-8_1Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A pair of rational double sequences
- On a new method of the testing hypothesis of equality of two Bernoulli regression functions for group observations
- Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
- A Robin boundary value problem for the Cauchy–Riemann operator in a ring domain
- Particular solutions of equations with multiple characteristics expressed through hypergeometric functions
- One remark on the inverse scattering problem for the perturbed Stark operator on the semiaxis
- On a geometric statement of Ramsey type
- Positive answer to the invariant and hyperinvariant subspaces problems for hyponormal operators
- Approximation on a new class of Szász–Mirakjan operators and their extensions in Kantorovich and Durrmeyer variants with applicable properties
- Regularity properties of nonlocal fractional differential equations and applications
- Solutions of a singular integro-differential equation related to the adhesive contact problems of elasticity theory
- Positive periodic solutions to the forced non-autonomous Duffing equations
- Absolute convergence factors of Lipschitz class functions for general Fourier series
Articles in the same Issue
- Frontmatter
- A pair of rational double sequences
- On a new method of the testing hypothesis of equality of two Bernoulli regression functions for group observations
- Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
- A Robin boundary value problem for the Cauchy–Riemann operator in a ring domain
- Particular solutions of equations with multiple characteristics expressed through hypergeometric functions
- One remark on the inverse scattering problem for the perturbed Stark operator on the semiaxis
- On a geometric statement of Ramsey type
- Positive answer to the invariant and hyperinvariant subspaces problems for hyponormal operators
- Approximation on a new class of Szász–Mirakjan operators and their extensions in Kantorovich and Durrmeyer variants with applicable properties
- Regularity properties of nonlocal fractional differential equations and applications
- Solutions of a singular integro-differential equation related to the adhesive contact problems of elasticity theory
- Positive periodic solutions to the forced non-autonomous Duffing equations
- Absolute convergence factors of Lipschitz class functions for general Fourier series