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11 papers
Corrigendum and Addendum to "Fra\"ıssé's Conjecture and big Ramsey degrees of structures admitting finite monomorphic decomposition''
Dragan Mašulović
In Section 6 of the paper ``Fra\"ıssé's Conjecture and big Ramsey degrees of structures admitting finite monomorphic decomposition'', we applied the methods developed in earlier se…
Big Ramsey combinatorics of the Cantor set and a simple proof of Blass' perfect set theorem
Dragan Mašulović
In this paper we present a simple approach to big Ramsey combinatorics of the Cantor set . Using Infinite Dual Ramsey Theorem of Carlson and Simpson, we show that , viewe…
On Ramsey degrees, compactness and approximability
Dragan Mašulović
One of the consequences of the Compactness Principle in structural Ramsey theory is that the small Ramsey degrees cannot exceed the corresponding big Ramsey degrees, thereby justif…
Classes of finite relational structures over finite languages have dual Ramsey degrees
Aleksa Džuklevski, Dragan Mašulović
Classical Ramsey theory has successfully extended to relational structures, yielding a wealth of results that have profoundly influenced other areas of mathematics. Interestingly,…
Tukey reducibility for categories -- In search of the strongest statement in finite Ramsey theory
Keegan Dasilva Barbosa, Dragan Mašulović
Every statement of the Ramsey theory of finite structures corresponds to the fact that a particular category has the Ramsey property. We can, then, compare the strength of Ramsey s…
Deducibility in Sudoku
Dragan Mašulović
In this paper we provide a formalism, Sudoku logic, in which a solution is logically deducible if for every cell of the grid we can provably exclude all but a single option. We pro…
Ramsey degrees and entropy of combinatorial structures
Dragan Mašulović
Close connections between various notions of entropy and the apparatus of category theory have been observed already in the 1980s and more vigorously developed in the past ten year…
Ramsey properties of products and pullbacks of categories and the Grothendieck construction
Dragan Mašulović
In this paper we provide purely categorical proofs of two important results of structural Ramsey theory: the result of M.\ Sokić that the free product of Ramsey classes is a Ramsey…
The Kechris-Pestov-Todor\vcević correspondence from the point of view of category theory
Dragan Mašulović
The Kechris-Pestov-Todorčević correspondence (KPT-correspondence for short) is a surprising correspondence between model theory, combinatorics and topological dynamics. In this pap…
Big Ramsey spectra of countable chains
Dragan Mašulović
A big Ramsey spectrum of a countable chain (i.e. strict linear order) C is a sequence of big Ramsey degrees of finite chains computed in C. In this paper we consider big Ramsey spe…
Countable ordinals and big Ramsey degrees
Dragan Mašulović, Branislav Šobot
In this paper we consider big Ramsey degrees of finite chains in countable ordinals. We prove that a countable ordinal has finite big Ramsey degrees if and only if it is smaller th…