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pro vyhledávání: '"Kossak, Roman"'
Autor:
Abdul-Quader, Athar, Kossak, Roman
The lattice problem for models of Peano Arithmetic ($\mathsf{PA}$) is to determine which lattices can be represented as lattices of elementary submodels of a model of $\mathsf{PA}$, or, in greater generality, for a given model $\mathcal{M}$, which la
Externí odkaz:
http://arxiv.org/abs/2406.06338
Autor:
Kossak, Roman
In September of 1959, at the conference on Infinitistic Methods in Warsaw, Ernst Specker presented a joint paper with Robert MacDowell in which the authors proved that every model of Peano Arithmetic has an elementary extension such that all new elem
Externí odkaz:
http://arxiv.org/abs/2208.03156
Autor:
Kossak, Roman
This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of nonstandard models.
Externí odkaz:
http://arxiv.org/abs/2205.06022
Autor:
Kossak, Roman, Wcisło, Bartosz
We introduce a tool for analysing models of $\textnormal{CT}^-$, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan's theorem that arithmetical part of models of $\textnormal{PA}$ are recursively saturated. We use
Externí odkaz:
http://arxiv.org/abs/1810.07437
Autor:
Abdul-Quader, Athar, Kossak, Roman
A subset of a model of ${\sf PA}$ is called neutral if it does not change the $\mathrm{dcl}$ relation. A model with undefinable neutral classes is called neutrally expandable. We study the existence and non-existence of neutral sets in various models
Externí odkaz:
http://arxiv.org/abs/1712.06503
Autor:
Kossak, Roman
Publikováno v:
Studia Semiotyczne / Semiotic Studies. 34(1):5-8
Externí odkaz:
https://www.ceeol.com/search/article-detail?id=914788
Autor:
Harris, Michael1 harris@math.columbia.edu
Publikováno v:
Mathematical Intelligencer. Jun2019, Vol. 41 Issue 2, p82-84. 3p.
Autor:
Coskey, Samuel, Kossak, Roman
Publikováno v:
Bulletin of symbolic logic 16(3):345-358, 2010
We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic are Borel;
Externí odkaz:
http://arxiv.org/abs/0908.1718
Autor:
Kossak, Roman
Publikováno v:
The American Mathematical Monthly, 1996 Dec 01. 103(10), 846-853.
Externí odkaz:
https://www.jstor.org/stable/2974609