Výsledky vyhledávání - "Asger Törnquist"

Set Theory and a Model of the Mind in Psychology

Publikováno v: Törnquist, A D & Mammen, J 2022, ' Set Theory and a Model of the Mind in Psychology ', Review of Symbolic Logic . https://doi.org/10.1017/S1755020322000107
Törnquist, A & Mammen, J 2022, ' Set Theory and a Model of the Mind in Psychology ', Review of Symbolic Logic . https://doi.org/10.1017/S1755020322000107

We investigate the mathematics of a model of the human mind which has been proposed by the psychologist Jens Mammen. Mathematical realizations of this model consist of so-called \emph{Mammen spaces}, where a Mammen space is a triple $(U,\mathcal S,\m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::71ddd9aa6459748418927087e5760289
https://vbn.aau.dk/da/publications/d2143704-cd2e-4519-872d-fa7f3a6cdcb2

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Maximal almost disjoint families, determinacy, and forcing

Autor: Asger Törnquist, David Schrittesser, Karen Bakke Haga

Publikováno v: Bakke Haga, K, Schrittesser, D & Törnquist, A 2022, ' Maximal almost disjoint families, determinacy, and forcing ', Journal of Mathematical Logic, vol. 22, no. 1, 2150026, pp. 1-42 . https://doi.org/10.1142/S0219061321500264

We study the notion of $\mathcal J$-MAD families where $\mathcal J$ is a Borel ideal on $\omega$. We show that if $\mathcal J$ is an arbitrary $F_\sigma$ ideal, or is any finite or countably iterated Fubini product of $F_\sigma$ ideals, then there ar

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6f3bc1bc83ee162424d9919fd7a814f
https://doi.org/10.1142/s0219061321500264

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The Borel complexity of von Neumann equivalence

Autor: Inessa Moroz, Asger Törnquist

Publikováno v: Moroz, I & Törnquist, A 2021, ' The Borel complexity of von Neumann equivalence ', Annals of Pure and Applied Logic, vol. 172, no. 5, 102913 . https://doi.org/10.1016/j.apal.2020.102913

We prove that for a countable discrete group Γ containing a copy of the free group F n , for some 2 ≤ n ≤ ∞ , as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6ee9ee03fdd2d81820e0d886ca0e58f7
https://curis.ku.dk/portal/da/publications/the-borel-complexity-of-von-neumann-equivalence(4a422a57-e7cf-4580-97d0-9434620c9148).html

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Unitarizability, Maurey–Nikishin factorization, and Polish groups of finite type

Autor: Yasumichi Matsuzawa, Asger Törnquist, Hiroshi Ando, Andreas Thom

Publikováno v: Journal für die reine und angewandte Mathematik (Crelles Journal)
Ando, H, Matsuzawa, Y, Thom, A & Törnquist, A D 2020, ' Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type ', Journal fuer die Reine und Angewandte Mathematik, vol. 758, pp. 223-251 . https://doi.org/10.1515/crelle-2017-0047

Let $\Gamma$ be a countable discrete group, and let $\pi\colon \Gamma\to {\rm{GL}}(H)$ be a representation of $\Gamma$ by invertible operators on a separable Hilbert space $H$. We show that the semidirect product group $G=H\rtimes_{\pi}\Gamma$ is SIN

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c550e2c67ca1c739e9acd58bdf4207bb
https://doi.org/10.1515/crelle-2017-0047

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The Ramsey property implies no mad families

Autor: Asger Törnquist, David Schrittesser

Publikováno v: Schrittesser, D & Törnquist, A 2019, ' The Ramsey property implies no mad families ', Proceedings of the National Academy of Sciences of the United States of America, vol. 116, no. 38, pp. 18883-18887 . https://doi.org/10.1073/pnas.1906183116

We show that if all collections of infinite subsets of $\N$ have the Ramsey property, then there are no infinite maximal almost disjoint (mad) families. This solves a long-standing problem going back to Mathias \cite{mathias}. The proof exploits an i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51574e16cb7e76bc2c0b4e424c69d9f0
https://curis.ku.dk/ws/files/229102859/OA_The_Ramsey_property_implies_no_mad_families.pdf

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Definability and almost disjoint families

Autor: Asger Törnquist

We show that there are no infinite maximal almost disjoint ("mad") families in Solovay's model, thus solving a long-standing problem posed by A.D.R. Mathias in 1967. We also give a new proof of Mathias' theorem that no analytic infinite almost disjoi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::20ea69ae66346a292141adf673c47629
https://resolver.caltech.edu/CaltechAUTHORS:20180327-083321909

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THE COUNTERPARTS TO STATEMENTS THAT ARE EQUIVALENT TO THE CONTINUUM HYPOTHESIS

Autor: Asger Törnquist, William Weiss

Publikováno v: The Journal of Symbolic Logic. 80:1075-1090

We consider natural ${\rm{\Sigma }}_2^1$ definable analogues of many of the classical statements that have been shown to be equivalent to CH. It is shown that these ${\rm{\Sigma }}_2^1$ analogues are equivalent to that all reals are constructible. We

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e8463c4b71141f31fd9403d21be6bac8
https://doi.org/10.1017/jsl.2014.20

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Template iterations and maximal cofinitary groups

Autor: Vera Fischer, Asger Törnquist

Publikováno v: Fundamenta Mathematicae. 230:205-236

The main result of the present paper is that $\mathfrak a_g$, the minimal size of maximal cofinitary group, can be of countable cofinality. To prove this we define a natural poset for adding a maximal cofinitary group of a given cardinality, which en

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fcdb8f1697fdb9811ca998c48bc45bd4
https://doi.org/10.4064/fm230-3-1

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Non-classification of free Araki-Woods factors and $\tau$-invariants

Autor: Román Sasyk, Stefaan Vaes, Asger Törnquist

Publikováno v: Sasyk, R, Törnquist, A & Vaes, S 2019, ' Non-classification of free Araki-Woods factors and τ-invariants ', Groups, Geometry, and Dynamics, vol. 13, no. 4, pp. 1219-1234 . https://doi.org/10.4171/GGD/520
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Consejo Nacional de Investigaciones Científicas y Técnicas
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We define the standard Borel space of free Araki-Woods factors and prove that their isomorphism relation is not classifiable by countable structures. We also prove that equality of $\tau$-topologies, arising as invariants of type III factors, as well

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2ec9cc611d318bbd1f248c763be8c538
http://arxiv.org/abs/1708.07496

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