Statement:
Rasiowa-Sikorski Axiom: If \((B,\land,\lor)\) is a Boolean algebra, \(a\) is a non-zero element of \(B\), and \(\{X_n: n\in\omega\}\) is a denumerable set of subsets of \(B\) then there is a maximal filter \(F\) of \(B\) such that \(a\in F\) and for each \(n\in\omega\), if \(X_n\subseteq F\) and \(\bigwedge X_n\) exists then \(\bigwedge X_n \in F\).
Howard_Rubin_Number: 345
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Rasiowa-Sikorski-1950: A proof of the completeness theorem of Gödel
Morillon-1988: Topologie, Analyse Nonstandard et Axiome du Choix
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 345 A |
Morillon [1988]
Goldblatt [1985]
|
|
| 345 B |
Morillon [1988]
|
|
| 345 C | Every bounded, distributive lattice has the strong Rasiowa-Sikorski property. |
Morillon [1988]
Note [71] |
| 345 D | Every bounded, distributive lattice has the Rasiowa-Sikorski property. |
Morillon [1988]
Note [71] |
| 345 E | Every Boolean algebra has the Rasiowa-Sikorski property. |
Morillon [1988]
Note [71] |