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- Title
HYPERFINITE LOGICS AND NON-STANDARD EXTENSIONS OF BOOLEAN ALGEBRAS.
- Authors
Ferenczi, Miklós
- Abstract
Infinitary propositional logics, i.e., propositional logics with infinite conjunction and disjunction, have some deficiencies, e.g., these logics fail to be compact or complete, in general. Such kind of infinitary propositional logics are introduced, called hyperfinite logics, which are defined in a non-standard framework of non-standard analysis and have hyperfinite conjunctions and disjunctions. They have more nice properties than infinitary logics have, in general. Furthermore, non-standard extensions of Boolean algebras are investigated. These algebras can be regarded as algebraizations of hyperfinite logics, they have several unusual properties. These Boolean algebras are closed under the hyperfinite sums and products, they are representable by hyperfinitely closed Boolean set algebras and they are omega-compact. It is proved that standard Boolean algebras are representable by Boolean set algebras with a hyperfinite unit.
- Subjects
NONSTANDARD mathematical analysis; LOGIC; BOOLEAN algebra
- Publication
Publications de l'Institut Mathématique, 2020, Vol 107, Issue 121, p53
- ISSN
0350-1302
- Publication type
Article
- DOI
10.2298/PIM2021053F