## Refutation of a 'concrete' Rauszer Boolean Algebra Generated by a Preorder

**Authors:** Colin James III

From the 11 equations tested, we refute 13 artifacts:
1. a condition for "an existential quantifier ∃ … on a Boolean algebra";
2. "a quantifier ∃ as closure operator on B, for which every open element is closed";
3. the interior operator on abstract topological Boolean algebra;
4. the kernel of a homomorphism from a Heyting algebra into another as a filter;
5. deductive systems and filters as equivalent;
6. the atomic definition of p ≤ ∃p in Halmos algebra;
7. a ‘concrete’ Rauszer Boolean algebra;
8. two conditions for the definition of a filter (and Heyting algebra using the filter);
9. a De Morgan algebra as a Kleene algebra;
10. equivalences of symmetrical Heyting algebras;
11. equivalences in Heyting algebras;
12. intuitionistic implication of intuitionistic logic; and
13. a theorem and a proposition of Nelson algebras.
As a result, the following seven areas are non tautologous fragments of the universal logic VŁ4:
1. Topological Boolean algebra;
2. Heyting algebra;
3. Intuitionistic logic;
4. Halmos algebra;
5. Rauszer algebra;
6. Kleene algebra; and
7. Nelson algebra.

**Comments:** 5 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

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### Submission history

[v1] 2019-05-27 21:13:09

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