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63 Years of the MacDowell-Specker Theorem
Roman Kossak
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…
Undefinability and Absolute Undefinability in Arithmetic
Roman Kossak
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 mod…
Disjunctions with stopping condition
Roman Kossak, Bartosz Wcisło
We introduce a tool for analysing models of , the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan's theorem that arithmetical…
Neutrally Expandable Models of Arithmetic
Athar Abdul-Quader, Roman Kossak
A subset of a model of is called neutral if it does not change the relation. A model with undefinable neutral classes is called neutrally expandable. We s…
The complexity of classification problems for models of arithmetic
Samuel Coskey, Roman Kossak
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 ari…