Editing Interior algebra (section)

==Metamathematics==
Grzegorczyk proved the [[first-order theory]] of closure algebras [[decision problem|undecidable]].<ref>[[Andrzej Grzegorczyk]] (1951), "Undecidability of some topological theories," ''[[Fundamenta Mathematicae]] 38'': 137–52.</ref><ref>According to footnote 19 in McKinsey and Tarski, 1944, the result had been proved earlier by [[Stanisław Jaśkowski]] in 1939, but remained unpublished and not accessible ''in view of the present [at the time] war conditions''.</ref> Naturman demonstrated that the theory is [[hereditarily undecidable]] (all its subtheories are undecidable) and demonstrated an infinite [[chain (order theory)|chain]] of elementary classes of interior algebras with hereditarily undecidable theories.