Adam Bartoš

bartos at math dot cas dot cz

• a researcher at the Institute of Mathematics of the Czech Academy of Sciences
• interested in generic mathematical structures / Fraïssé theory, category theory, mathematical logic, topology → [Publications]

Additional materials

Category-theoretic Fraïssé theory: an overview

Fraïssé theory allows constructing and studying “large” symmetric structures through their “small” approximations. It allows a category-theoretic formultion that abstracts both from classes of first-order structures with embeddings and from the projective Fraïssé theory.

• Abstract for my TACL 2024 – can be used as a quick summary of the abstract framework
• Slides for my TACL 2024 talk
• Slides for my invited talk for the Conference on Generic Structures (2023)
• Slides for my Warsaw seminar talk (2023) – a gentle introduction, some overlap with the previous

Constructing compacta from posets and sequences of graphs

We develop two alternative approaches to projective Fraïssé theory – the approximate approach where we work directly with metrizable compacta and with approximate Fraïssé-theoretic notions, and the spectral approach where multivalued maps between graphs are allowed and the spectrum on an ω-poset takes place of the limit construction.

• Newer slides on the topic, presented at the Ostrava–Prague Seminar (2026)
• Abstract for my CT 2024 poster – summarizes approaches to projective Fraïssé theory
• Poster for CT 2024, updated for Łódź Logic Conference (2026)
• Slides for my Winter School 2024 talk on Fraïssé-like constructions of compacta
• Poster for the Workshop on the Frontiers of Set Theory (2023)

Preprints

• A. Bartoš, W. Kubiś, A. Kwiatkowska, M. Malicki
  Generic dc-automorphisms of two-sorted ultrametric space.
  33 pages. [arXiv]
• A. Bartoš, W. Kubiś, A. Kwiatkowska, M. Malicki
  Universal homogeneous two-sorted ultrametric spaces.
  47 pages. [arXiv]
• A. Bartoš, T. Bice, A. Vignati.
  Generic Compacta from Relations between Finite Graphs: Theory Building and Examples.
  63 pages. [arXiv]

Publications

1. A. Bartoš, W. Kubiś.
   Hereditarily indecomposable continua as generic mathematical structures.
   Selecta Math. (N.S.) 32 (2026), no. 1, Paper No. 14. [DOI] [arXiv]
2. A. Bartoš, W. Kubiś.
   Uncountable homogeneous structures.
   Ann. Pure Appl. Logic 177 (2026), 103649, 19 pages. [DOI] [arXiv]
3. A. Bartoš, T. Bice, A. Vignati.
   Constructing Compacta from Posets.
   Publ. Mat. 69 (2025), 217–265. [DOI] [arXiv]
4. A. Bartoš, T. Bice, K. Dasilva Barbosa, W. Kubiś.
   The weak Ramsey property and extreme amenability.
   Forum Math. Sigma 12 (2024), e96, 42 pages. [DOI] [arXiv]
5. C. Bargetz, A. Bartoš, W. Kubiś, F. Luggin.
   Homogeneous isosceles-free spaces.
   Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118 (2024), 118, 32 pages. [DOI] [arXiv]
6. A. Bartoš, J. Bobok, P. Pyrih, S. Roth, B. Vejnar.
   Constant slope, entropy and horseshoes for a map on a tame graph.
   Ergodic Theory Dynam. Systems 40 (2020), no. 11, 2970–2994. [DOI] [arXiv]
7. A. Bartoš.
   Borel complexity up to the equivalence.
   Topology Appl. 270 (2020), 107042, 13 pages. [DOI] [arXiv]
8. A. Bartoš, J. Bobok, J. van Mill, P. Pyrih, B. Vejnar.
   Compactifiable classes of compacta.
   Topology Appl. 266 (2019), 106836, 25 pages. [DOI] [arXiv]
9. A. Bartoš.
   Tree sums of maximal connected spaces.
   Topology Appl. 252 (2019), 50–71. [DOI] [arXiv]
10. T. Banakh, A. Bartoš.
    Lower separation axioms via Borel and Baire algebras.
    Serdica Math. J. 44 (2018), 155–176. [PDF] [arXiv]
11. A. Bartoš, R. Marciňa, P. Pyrih, B. Vejnar
    Incomparable compactifications of the ray with Peano continuum as remainder.
    Topology Appl. 208 (2016), 93–105. [DOI]
12. A. Bartoš.
    On n-thin dense sets in powers of topological spaces.
    Comment. Math. Univ. Carolin. 57, 1 (2016), 73–82. [DOI]

Thesis

My PhD thesis Families of connected spaces, supervised by Petr Simon and Benjamin Vejnar, and defended in September 2019, consists of the papers 4., 5., 6. and of an introduction providing more context and references. The following note summarizes an open question regarding our notion of compactifiable classes of compacta.