3 papers
math.LO2026
On a new theory of models for formal mathematical systems
Matthias Kunik
We study a new model theory for formal mathematical systems that we developed in a previous paper. We introduce isomorphic and homomorphic structures for formal languages, present…
math.LO2026
On the downward Löwenheim-Skolem Theorem for elementary submodels
Matthias Kunik
We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic appr…
math.LO2026
Reduced Set Theory
Matthias Kunik
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an int…