Uniform Density in Lindenbaum Algebras

Forcing with Propositional Lindenbaum Algebras

We prove equivalence between the forcing with propositional Lindenbaum algebras and the Cohen forcing with finite partial functions.

Lindenbaum Algebras and Partial Conservativity

A partial Lindenbaum algebra TA, where A is a theory extending Peano arithmetic and T G {LTn,£n}, is the full Lindenbaum algebra for A restricted to sentences in A provably equivalent to rn-sentences. Using a new result on pairs of partially conservative sentences, we show that Tl£ and E^ are not isomorphic.

M-IDEAL STRUCTURE IN UNIFORM ALGEBRAS

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).

Uniform Algebras on Curves

The proofs use the notion of analytic structure in a maximal ideal space. J. Wermer first obtained results along these lines and further contributions were made by E. Bishop and H. Royden and then by G. Stolzenberg [5] who proved STOLZENBERG'S THEOREM. Let XQC be a polynomially convex set. Let KQC be a finite union of Q-curves. Then (XKJK)*—X\JK is a {possibly empty) pure 1-dimensional analytic...

Sufficient Conditions for Density in Extended Lipschitz Algebras