absoluteness 1boolean algebras 1coherent separations 1forcing 1freese-nation property 1full symmetric groups 1model theory 1operator algebras 1projective algebras 1standard reconstruction 1weakly projective algebras 1
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math.LO2026
Approximate homomorphisms on orthomodular lattices
Tomasz Kania
The stability programme initiated by Ulam asks when approximate solutions to algebraic identities must lie near exact ones. For lattices, this leads to the question of when a map t…
math.LO2026
Characterising projective and weakly projective Boolean algebras by coherent Freese--Nation separations
Tomasz Kania, Andrzej Kucharski, SÅawomir Turek
The authors define a coherent finite‑separation strengthening of the Freese–Nation property and prove that a Boolean algebra is projective precisely when it has a meet‑closed decom…
math.LO2026
Canonical reconstruction and forcing absoluteness of standard structures
Tomasz Kania
The paper identifies a preservation principle that ensures the standard form of various algebraic and topological structures remains absolute between transitive models of set theor…