### Abstract

We present a collection of axiom systems for the construction of Boolean subalgebras of larger overall algebras. The subalgebras are defined as the range of a complement-like operation on a semilattice. This technique has been used, for example, with the antidomain operation, dynamic negation and Stone algebras. We present a common ground for these constructions based on a new equational axiomatisation of Boolean algebras.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session Subset_Boolean_Algebras

- Subset_Boolean_Algebras

### Depends on

- Stone Algebras

### Used by

- Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations

## Cite

×

Subset_Boolean_Algebras-AFP

    @article{Subset_Boolean_Algebras-AFP,
      author  = {Walter Guttmann and Bernhard Möller},
      title   = {A Hierarchy of Algebras for Boolean Subsets},
      journal = {Archive of Formal Proofs},
      month   = {January},
      year    = {2020},
      note    = {\url{https://isa-afp.org/entries/Subset_Boolean_Algebras.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

Download

## Download

× Download latest

Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 20, 2020 : Isabelle2020
- Jan 31, 2020 : Isabelle2019