Some theorems on universal algebras. III

Realizability algebras III: some examples

The notion of realizability algebra, which was introduced in [17, 18], is a tool to study the proof-program correspondence and to build new models of set theory, which we call realizability models of ZF. It is a variant of the well known notion of combinatory algebra, with a new instruction cc, and a new type for the environments. The sets of forcing conditions, in common use in set theory, are...

Fuzzy universal algebras on $L$-sets

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

Some Characterization Theorems for Infinitary Universal Horn Logic Without Equality

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...

Some Theorems on Coverings

Some Theorems on Continua

PROOF. Let {Gn} and {Hn} denote monotonie decreasing sequences of open sets which close down upon .Pi and F2 respectively. We may suppose that d and Hi are so chosen that G i # i = 0. Now, by Mullikin's theorem, there is a connected subset of C— C(Gw+27n) which has a limit point in Gn and a limit point in Hn. The closure of such a connected set is a subcontinuum of C which "extends" from Gn to ...