[PDF][PDF] Shelah's Main Gap and the generalized Borel-reducibility

M Moreno - Preprint, 2023 - miguelmath.com
We answer one of the main questions in generalized descriptive set theory, the Friedman-
Hyttinen-Kulikov conjecture on the Borel reducibility of the Main Gap. We show a correlation …

On unsuperstable theories in GDST

M Moreno - The Journal of Symbolic Logic, 2023 - cambridge.org
Abstract We study the $\kappa $-Borel-reducibility of isomorphism relations of complete first-
order theories by using coloured trees. Under some cardinality assumptions, we show the …

Fake reflection

G Fernandes, M Moreno, A Rinot - Israel Journal of Mathematics, 2020 - Springer
We introduce a generalization of stationary set reflection which we call filter reflection, and
show it is compatible with the axiom of constructibility as well as with strong forcing axioms …

A descriptive main gap theorem

F Mangraviti, L Motto Ros - Journal of Mathematical Logic, 2021 - World Scientific
Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov,
Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230 …

The isomorphism relation of theories with S-DOP in the generalised Baire spaces

M Moreno - Annals of Pure and Applied Logic, 2022 - Elsevier
We study the Borel-reducibility of isomorphism relations in the generalised Baire space κ κ.
In the main result we show for inaccessible κ, that if T is a classifiable theory and T′ is …

On -completeness of quasi-orders on

T Hyttinen, V Kulikov, M Moreno - arXiv preprint arXiv:1804.02213, 2018 - arxiv.org
We prove under $ V= L $ that the inclusion modulo the non-stationary ideal is a $\Sigma_1^
1$-complete quasi-order in the generalized Borel-reducibility hierarchy ($\kappa>\omega $) …

FROM REAL-LIFE TO VERY STRONG AXIOMS Classification problems in Descriptive Set Theory & regularity properties in Generalized Descriptive Set Theory

M Iannella - 2023 - air.uniud.it
This thesis is divided into three parts, the first and second ones focused on combinatorics
and classification problems on discrete and geometrical objects in the context of descriptive …

[PDF][PDF] Finding the main gap in the Borel-reducibility hierarchy

M Moreno - Helsingin Yliopisto, 2017 - helda.helsinki.fi
This research was supported by the DOCTORAL PROGRAMME IN MATHEMATICS AND
STATISTICS (Domast), to which I want to express my gratitude. Without their support it would …

[PDF][PDF] Tutorial on Generalized Descrptive Set Theory

M Moreno - 2023 - mathematik.univie.ac.at
This notes are based on a series of talks given at the Set Theory seminar of University of
Vienna. This notes are intended to be as close as possible to the transcripts of those …

[PDF][PDF] Isolation notions and construction of models

M Moreno - 2023 - miguelmath.com
This notes are based on a series of talks given at the Research Model Theory seminar of
University of Vienna. This notes are intended to be as close as possible to the transcripts of …