Abstract
The poset of copies of a relational structure 𝕏 is the partial order 〈ℙ(𝕏), ⊂〉, where
Funding statement: This research was supported by the Science Fund of the Republic of Serbia, Program IDEAS, Grant No. 7750027: Set-theoretic, model-theoretic and Ramsey-theoretic phenomena in mathematical structures: similarity and diversity–SMART.
(Communicated by David Buhagiar)
References
[1] Balcar, B.—Pelant, J.—Simon, P.: The space of ultrafilters on ℕ covered by nowhere dense sets, Fund. Math. 110(1) (1980), 11–24.Search in Google Scholar
[2] Balcar, B.—Simon, P.: Disjoint refinement. In: Handbook of Boolean algebras, Vol. 2 (J. D. Monk, R. Bonnet, eds.), North-Holland, Amsterdam, 1989, pp. 333–388.Search in Google Scholar
[3] Baumgartner, J. E.: All ℵ1-dense sets of reals can be isomorphic, Fund. Math. 79(2) (1973), 101–106.Search in Google Scholar
[4] Dushnik, B.—Miller, E. W.: Concerning similarity transformations of linearly ordered sets, Bull. Amer. Math. Soc. 46 (1940), 322–326.Search in Google Scholar
[5] Fraïssé, R.: Theory of Relations. Stud. Log. Found. Math., Vol. 145 (revised edition, with an appendix by Norbert Sauer), North-Holland, Amsterdam, 2000.Search in Google Scholar
[6] Frasnay, C.: Quelques problémes combinatoires concernant les ordres totaux et les relations monomorphes, Ann. Inst. Fourier (Grenoble) 15(2) (1965), 415–524.Search in Google Scholar
[7] Gibson, P. C.—Pouzet, M.—Woodrow, R. E.: Relational structures having finitely many full-cardinality restrictions, Discrete Math. 291(1–3) (2005), 115–134.Search in Google Scholar
[8] Hodges, W.—Lachlan, A. H.—Shelah, S.: Possible orderings of an indiscernible sequence, Bull. London Math. Soc. 9(2) (1977), 212–215.Search in Google Scholar
[9] Kechris, A. S.: Classical Descriptive Set Theory. Grad. Texts Math., Vol. 156, Springer-Verlag, 1995.Search in Google Scholar
[10] Kojman, M.—Shelah, S.: Fallen cardinals, Dedicated to Petr Vopěnka, Ann. Pure Appl. Logic 109(1–2) (2001), 117–129.Search in Google Scholar
[11] Kunen, K.: Set Theory. An Introduction to Independence Proofs. Stud. Logic Found. Math., Vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980.Search in Google Scholar
[12] Kurilić, M. S.: From A1 to D5 towards a forcing-related classification of relational structures, J. Symb. Log. 79(1) (2014), 279–295.Search in Google Scholar
[13] Kurilić, M. S.: Posets of copies of countable scattered linear orders, Ann. Pure Appl. Logic 165(3) (2014), 895–912.Search in Google Scholar
[14] Kurilić, M. S.: Forcing with copies of countable ordinals, Proc. Amer. Math. Soc. 143(4) (2015), 1771–1784.Search in Google Scholar
[15] Kurilić, M. S.: Different similarities, Arch. Math. Logic 54(7–8) (2015), 839–859.Search in Google Scholar
[16] Kurilić, M. S.: Vaught’s conjecture for monomorphic theories, Ann. Pure Appl. Logic 170(8) (2019), 910–920.Search in Google Scholar
[17] Kurilić, M. S.: Iterated reduced powers of collapsing algebras, Ann. Pure Appl. Logic 176(6) (2025), Art. No. 103567.Search in Google Scholar
[18] Kurilić, M. S.: Forcing with copies of uncountable ordinals, https://arxiv.org/pdf/2401.00302.Search in Google Scholar
[19] Kurilić, M. S.—Todorčević, S.: Forcing by non-scattered sets, Ann. Pure Appl. Logic 163 (2012), 1299–1308.Search in Google Scholar
[20] Laflamme, C.—Pouzet, M.—Woodrow, R.: Equimorphy: the case of chains, Arch. Math. Logic 56(7–8) (2017), 811–829.Search in Google Scholar
[21] Laver, R.: On Fraïssé’s order type conjecture, Ann. of Math. 93(2) (1971), 89–111.Search in Google Scholar
[22] Moore, J. T.: A five element basis for the uncountable linear orders, Ann. of Math. (2) 163(2) (2006), 669–688.Search in Google Scholar
[23] Pouzet, M.: Application de la notion de relation presque-enchaînable au dénombrement des restrictions finies d’une relation, Z. Math. Logik Grundlagen Math. 27(4) (1981), 289–332.Search in Google Scholar
[24] Rosenstein, J. G.: Linear Orderings. Pure Appl. Math., Vol. 98, Academic Press, Inc. Harcourt Brace Jovanovich Publishers, New York-London, 1982.Search in Google Scholar
[25] Shelah, S.: Power set modulo small, the singular of uncountable cofinality, J. Symbolic Logic 72(1) (2007), 226–242.Search in Google Scholar
[26] Sierpiński, W.: Cardinal and Ordinal Numbers. 2nd revised edition, Monografie Matematyczne, Vol. 34, Panstwowe Wydawnictwo Naukowe (PWN), Warsaw, 1965.Search in Google Scholar
[27] Simon, P.: Sacks forcing collapses c to b, Comment. Math. Univ. Carolin. 34(4) (1993), 707–710.Search in Google Scholar
[28] Solovay, R. M.: A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1–56.Search in Google Scholar
© 2025 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
- Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
- Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations