Timeline for Sigma-complete Lindenbaum algebras?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 1, 2014 at 12:47 | comment | added | Joel David Hamkins | Or: the theory $T$ asserting that one of $n$ distinct finitely-axiomatizable complete theories holds. Each such theory is an atom, and every statement will be a join of atoms. | |
| Apr 1, 2014 at 11:30 | comment | added | Joel David Hamkins | Yes, I had noticed that, but of course, the finite Boolean algebras are trivially realized as Lindenbaum algebras. For example, in the theory asserting that there are exactly $n$ objects, with $n$ distinct constants $c_i$ and one more constant $d$, which must be one of the $c_i$. The assertions $d=c_i$ are atoms, and every assertion is some Boolean combination of the these atoms. | |
| Apr 1, 2014 at 10:59 | comment | added | Andrej Bauer | OP does not say "infinte" anywhere... | |
| Mar 31, 2014 at 21:21 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |