A note on the generalized continuum hypothesis. II.

The Generalized Continuum Hypothesis Revisited Sh460

A Note on Artinianess of Certain Generalized

Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-modules and are Artinian for all integers i and j, whenever and . Also we will show that if a is principal, then the R-modules and ...

A Note on Bjerknes' Hypothesis . . .

Bryan. K. and Stouffer. R.. 1991. A note on Bjerknes' hypothesis for North Atlantic VOiriOibililY. J. ~IOIr. SYSI.. 1: 229-241 On decadal time-scales the historical surface temperature record over land in the Northern Hemisphere is dominated by polar amplified variations. These variations are coherent ~.ith SST anomalies concentrated in the Northwest Atlantic. but extending with lesser amplitud...

The Continuum Hypothesis, Part II, Volume 48, Number 7

Introduction In the first part of this article, I identified the correct axioms for the structure 〈P(N),N,+, ·,∈〉 , which is the standard structure for Second Order Number Theory. The axioms, collectively “Projective Determinacy”, solve many of the otherwise unsolvable, classical problems of this structure. Actually working from the axioms of set theory, ZFC, I identified a natural progression ...

The Continuum Hypothesis

The continuum hypotheses (CH) is one of the most central open problems in set theory, one that is important for both mathematical and philosophical reasons. The problem actually arose with the birth of set theory; indeed, in many respects it stimulated the birth of set theory. In 1874 Cantor had shown that there is a one-to-one correspondence between the natural numbers and the algebraic number...