## S(z A y ) z S(A), by (c) * S(z) A S(Y) 2 S(A) e S(x) 2 S(A) and S(y) 2 S(A) e C ( s ) s C ( A ) 'and C ( y ) E C ( A ) , by (c) o x β¬ C ( A ) and Y E C ( A ) . Now every ultrafilter is consistent and closed with respect to C, since if U is an ultrafilter and C ( U ) = X , then C({,uu,, . . ., ,
β¦ LIBER β¦
Boolean algebra and syllogism
β Scribed by V. A. Bocharov
- Publisher
- Springer Netherlands
- Year
- 1986
- Tongue
- English
- Weight
- 642 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0039-7857
No coin nor oath required. For personal study only.
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## Abstract If __ΞΊ__ is an infinite cardinal, a complete Boolean algebra B is called __ΞΊ__βsupported if for each sequence γ__b~Ξ²~__ : __Ξ²__ < __ΞΊ__γ of elements of B the equality $ \wedge$~__Ξ±__<__ΞΊ__~ $ \vee$~__Ξ²__>__Ξ±__~ __b~Ξ²~__ = $ \vee$ $ \wedge$~__Ξ²__β__A__~ __b__~__Ξ²__~ holds. Combinatorial