Miloš S. Kurilić

activity

20132026

most citedPosets of Copies of Countable Scattered Linear Orders

5 citations · 9 across the 13 of their papers we have counts for

collaborators

23 papers

math.LO2026

Vaught's Conjecture for Sums of Products of Rooted Trees

Miloš S. Kurilić

We confirm Vaught's conjecture for each partial order $X = \sum_{I} \prod_{j < m_{i}} X_{i, j}$ from the closure $\langle \langle {\mathcal C}^{\rm rt}\rangle…

math.LO2024

Copies of Monomorphic Structures

Miloš S. Kurilić

The poset of copies of a relational structure $X$ is the partial order $⟨ P (X), \subset ⟩$ , where ${\mathbb P} ({\mathbb X})=\{ Y\subset…

math.LO2023

Posets of Copies of Countable Ultrahomogeneous Tournaments

Miloš S. Kurilić, Stevo Todorčević

The poset of copies of a relational structure $X$ is the partial order ${\mathbb P} ({\mathbb X} ) := \langle \{ Y \subset X: {\mathbb Y} \cong {\mathbb X}\}, \subset \ra…

math.LO2023

Back and Forth Systems Witnessing Irreversibility

Miloš S. Kurilić

If $L$ is a relational language, then an $L$ -structure $X = ⟨ X, ρ ˉ ⟩$ is reversible iff there is no interpretation $σ ˉ  ρ ˉ$ such that the…

math.LO2022

Sharp Vaught's Conjecture for Some Classes of Partial Orders

Miloš S. Kurilić

Matatyahu Rubin has shown that a sharp version of Vaught's conjecture, $I (T, ω) \in {0, 1, c}$ , holds for each complete theory of linear order $T$ …

math.LO2019

Vaught's Conjecture for Almost Chainable Theories

Miloš S. Kurilić

A structure $Y$ of a relational language $L$ is called almost chainable iff there are a finite set $F \subset Y$ and a linear order $<$ on the set $Y ∖ F$ such tha…

math.LO2019

Antichains of Copies of Ultrahomogeneous Structures

Miloš S. Kurilić, Boriša Kuzeljević

We investigate possible cardinalities of maximal antichains in the poset of copies $⟨ P (X), \subset ⟩$ of a countable ultrahomogeneous relational structu…

math.LO2018

Vaught's Conjecture for Monomorphic Theories

Miloš S. Kurilić

A complete first order theory of a relational signature is called monomorphic iff all its models are monomorphic (i.e. have all the $n$ -element substructures isomorphic, for each p…

math.LO2018

Reversibility of Extreme Relational Structures

Miloš S. Kurilić, Nenad Morača

A relational structure $X$ is called reversible iff each bijective homomorphism from $X$ onto $X$ is an isomorphism, and linear orders are prototypical e…

math.LO2017

Reversible Disjoint Unions of Well Orders and Their Inverses

Miloš S. Kurilić, Nenad Morača

A poset $P$ is called reversible iff every bijective homomorphism $f : P \to P$ is an automorphism. Let $W$ and ${\mathcal{W}} ^*…

math.LO2017

Reversibility of Disconnected Structures

Miloš S. Kurilić, Nenad Morača

A relational structure is called reversible iff every bijective endomorphism of that structure is an automorphism. We give several equivalents of that property in the class of disc…

math.LO2014★ 2 cited

Different Similarities

Miloš S. Kurilić

We establish the hierarchy among twelve equivalence relations (similarities) on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relati…

math.LO2014

Copies of the Random Graph: the 2-localization

Miloš S. Kurilić, Stevo Todorčević

Let $G$ be a countable graph containing a copy of the countable random graph (Erdős-Rényi graph, Rado graph), $E mb (G)$ the monoid of its self-embeddings, ${\mathbb P} (G)=\{f[G]:…

math.LO2014

Copies of the Random Graph

Miloš S. Kurilić, Stevo Todorčević

Let $(R, \sim)$ be the Rado graph, $E mb (R)$ the monoid of its self-embeddings, $Π (R) = {f [R] : f \in E mb (R)}$ the set of copies of $R$ contained in $R$ , and $I_{R}$ the…

math.LO2013

Isomorphic and Strongly Connected Components

Milos Kurilic

We study the partial orderings of the form $⟨ P (X), \subset ⟩$ , where $X$ is a binary relational structure with the connectivity compone…

math.LO2013

Maximal Chains of Isomorphic Subgraphs of Countable Ultrahomogeneous Graphs

Milos S. Kurilic, Borisa Kuzeljevic

For a countable ultrahomogeneous graph G let P(G) denote the collection of domains of subgraphs of G isomorphic to G. The order types of maximal chains in the set P(G) U ø ordered…

math.LO2013

Forcing With Copies of Countable Ordinals

Milos Kurilic

Let αbe a countable ordinal and ¶(α) the collection of its subsets isomorphic to α. We show that the separative quotient of the set ¶(α) ordered by the inclusion is isomorphic to a…

math.LO2013

Four Games on Boolean Algebras

Milos S. Kurilic, Boris Sobot

The games G_2 and G_3 are played on a complete Boolean algebra B in ω-many moves. At the beginning White picks a non-zero element p of B and, in the n-th move, White picks a positi…

math.LO2013★ 1 cited

Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous Partial Orders

Milos S. Kurilic, Borisa Kuzeljevic

We investigate the poset (P(X),\subset), where P(X) is the set of isomorphic suborders of a countable ultrahomogeneous partial order X. For X different from (resp. equal to) a coun…

math.LO2013★ 5 cited

Posets of Copies of Countable Scattered Linear Orders

Milos S. Kurilic

We show that the separative quotient of the poset (P(L),\subset) of isomorphic suborders of a countable scattered linear order L is σ-closed and atomless. So, under the CH, all the…

math.LO2013

Maximally Embeddable Components

Milos S. Kurilic

We investigate the partial orderings of the form (P(X),\subset), where X is a countable binary relational structure and P(X) the set of the domains of its isomorphic substructures…

math.LO2013★ 1 cited

From A1 to D5: Towards a Forcing-Related Classification of Relational Structures

Milos S. Kurilic

We investigate the partial orderings of the form (P(X),\subset), where X is a relational structure and P(X) the set of the domains of its isomorphic substructures. A rough classifi…

math.GN2013

A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube

Miloš S. Kurilić, Aleksandar Pavlović

We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $λ_{s}$ (the algebraic convergence) and $λ_{l s}$ on B generalizing t…