Abstract
There is a Mazurkiewicz set in the Cohen–Halpern–Levy model.
Funding source: Shota Rustaveli National Science Foundation
Award Identifier / Grant number: YS-21-1667
Funding statement: This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG), YS-21-1667.
References
[1] M. Beriashvili, R. Schindler, L. Wu and L. Yu, Hamel bases and well-ordering the continuum, Proc. Amer. Math. Soc. 146 (2018), no. 8, 3565–3573. 10.1090/proc/14010Search in Google Scholar
[2] B. Chad, R. Knight and R. Suabedissen, Set-theoretic constructions of two-point sets, Fund. Math. 203 (2009), no. 2, 179–189. 10.4064/fm203-2-4Search in Google Scholar
[3] B. R. Gelbaum and J. M. H. Olmsted, Counterexamples in Analysis, Holden-Day, San Francisco, 1964. Search in Google Scholar
[4] A. B. Kharazishvili, Nonmeasurable Sets and Functions, North-Holland Math. Stud. 195, Elsevier Science, Amsterdam, 2004. Search in Google Scholar
[5] A. B. Kharazishvili, Elements of Combinatorial Geometry. Part I, Georgian National Academy of Sciences, Tbilisi, 2016. Search in Google Scholar
[6] D. G. Larman, A problem of incidence, J. Lond. Math. Soc. 43 (1968), 407–409. 10.1112/jlms/s1-43.1.407Search in Google Scholar
[7] S. Mazurkiewicz, Sur un ensemble plan qui a avec chaque droite deux et seulement deux points communs, C. R. Varsovie 7 (1914), 382–384. Search in Google Scholar
[8] A. W. Miller, Infinite combinatorics and definability, Ann. Pure Appl. Logic 41 (1989), no. 2, 179–203. 10.1016/0168-0072(89)90013-4Search in Google Scholar
[9] A. W. Miller, The axiom of choice and two-point sets in the plane, preprint (2008), https://people.math.wisc.edu/~miller/res/two-pt.pdf. Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Spectral description of Fredholm operators via polynomially Riesz operators perturbation
- On the estimation of the Bernoulli regression function using Bernstein polynomials for group observations
- Mazurkiewicz sets with no well-ordering of the reals
- On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded
- On the generalization of the Janashia–Lagvilava method for arbitrary fields
- On a boundary-domain integral equation system for the Robin problem for the diffusion equation in non-homogeneous media
- Classical inequalities for pseudo-integral
- The boundary value problem for one class of higher-order nonlinear partial differential equations
- On 𝑆-weakly prime ideals of commutative rings
- Necessary and sufficient conditions of optimality for second order discrete and differential inequalities
- Perturbation results and forward order law for the Moore–Penrose inverse in rings with involution
- On 𝑇1- and 𝑇2-productable compact spaces
- On a Riemann--Hilbert boundary value problem for (ϕ,ψ)-harmonic functions in ℝ m
- On an equation by primes with one Linnik prime
- Differentiable functions and their Fourier coefficients
Articles in the same Issue
- Frontmatter
- Spectral description of Fredholm operators via polynomially Riesz operators perturbation
- On the estimation of the Bernoulli regression function using Bernstein polynomials for group observations
- Mazurkiewicz sets with no well-ordering of the reals
- On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded
- On the generalization of the Janashia–Lagvilava method for arbitrary fields
- On a boundary-domain integral equation system for the Robin problem for the diffusion equation in non-homogeneous media
- Classical inequalities for pseudo-integral
- The boundary value problem for one class of higher-order nonlinear partial differential equations
- On 𝑆-weakly prime ideals of commutative rings
- Necessary and sufficient conditions of optimality for second order discrete and differential inequalities
- Perturbation results and forward order law for the Moore–Penrose inverse in rings with involution
- On 𝑇1- and 𝑇2-productable compact spaces
- On a Riemann--Hilbert boundary value problem for (ϕ,ψ)-harmonic functions in ℝ m
- On an equation by primes with one Linnik prime
- Differentiable functions and their Fourier coefficients