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Notes on ultrafilter extensions of almost bounded structures
Zalán Molnár
We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one bin…
Ultrafilter extensions of bounded graphs are elementary
Zalán Molnár
The main motivation of this paper is the study of first-order model theoretic properties of structures having their roots in modal logic. We will focus on the connections between u…
On the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs without AC
Amitayu Banerjee, Alexa Gopaulsingh, Zalán Molnár
In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs int…
Varieties of modal algebras without the congruence extension property
Zalán Gyenis, Zalán Molnár
In a recent paper, Krawczyk proved that there are continuum many axiomatic extensions of global consequence associated with the modal system that do not admit the local deducti…