Axiom of countable choice

The axiom of countable choice or axiom of denumerable choice is an axiom of set theory similar to the axiom of choice. It states that a countable collection of sets must have a choice function. Paul Cohen showed that this is not provable in ZF. This axiom is required for the devlopment of analysis; in particular, many results depend on having a choice function for a countable set of real numbers.

The axiom of choice clearly implies the axiom of dependent choice, and the axiom of dependent choice is sufficent to show the axiom of choice. The axiom of countable choice is strictly weaker than each of these axioms.



In the News

After Surviving Breast Cancer, Women Face Increased Risk Of Heart Dise
Women who overcome breast cancer have every reason to celebrate. But a heart filled with joy may also be a heart damaged by life-saving cancer therapies, a growing body of research shows. Breast cancer is the most common form of cancer among American women, accounting for more than 200,000 new cases each year. Thanks to new and better therapies, death rates from breast cancer are falling dramatically -- by nearly 24 percent between 1990 and 2000, for example.

[Funny] Wis. Police Search for Wandering Kangaroo
Iowa county deputies are - for the first time ever - searching not for a emu or bobcat, but a 150-lb, reddish-brown kangaroo...

Eocene Plant Diversity At Laguna Del Hunco And Río Pichileufú, Patagon
South American floras are famous for their high species diversity. However, because of the undersampled South American plant-fossil record, remarkably little is known about how long this floral richness has existed.

University Of Ulster Researcher Unravels Mystery Of Falkland Islands
A researcher from the University of Ulster is finding out what the climate and landscape was like thousands of years ago from a unique rock formation in the Falkland Islands.

California Coastal Cleanup Day
This annual event held in mid-September "is the premier volunteer event focused on the marine environment in the country. On this day, 50,000 volunteers turn out to over 700 cleanup sites statewide to conduct what has been hailed by the Guinness Book of World Records as 'the largest garbage collection' (1993)."The site features a list of events around the state and material about the "Adopt-A-Beach"program. From the California Coastal Commission.

UCLA Researchers Discover New Method To Generate Human Bone
By studying diseases in which the human body generates too much bone, UCLA researchers have discovered and isolated a natural molecule that can be used to heal fractures and generate new bone growth in patients who lack it.

Why Is The Hercules Dwarf Galaxy So Flat?
Through some of the very first scientific observations with the brand-new Large Binocular Telescope in Arizona, astronomers have found that a recently discovered tiny companion galaxy to our Milky Way, named the Hercules Dwarf Galaxy, has truly exceptional properties: while basically all of its known peers in the realm of these tiny dwarf galaxies are rather round, this galaxy at a distance of 430,000 light years appears highly flattened, either the shape of a disk or of a cigar.

Stem Cells In Degenerating Spinal Discs Discovered, Potential For Repa
Orthopedic researchers have for the first time found stem cells in both degenerated adult intervertebral discs of the human spine and in discs of animals. The scientists isolated cells from discarded disc tissue that could still proliferate, noting that under certain conditions, the cells could be coaxed to form bone, cartilage or fat. The work suggests that such cells might someday be used to help repair degenerating discs and remedy lower back and neck pain.

First Familial Pancreatic Cancer Gene Identified
At least 10 percent of pancreatic cancers are thought to be familial, i.e., caused by inherited genetic mutations. The responsible genes have so far remained elusive, but one of the research teams that had been on a pancreatic cancer gene hunt for years now reports success: Teri Brentnall (University of Washington), David Whitcomb (University of Pittsburgh), and colleagues publish the identification of the palladin gene as the one mutated in a large family they had been studying for a while.

NASA Rovers' Adventures On Mars Continue
NASA lit a birthday candle for its twin Mars Exploration Rovers (MER) Spirit and Opportunity. The Spirit rover begins its second year on Mars investigating puzzling rocks unlike any found earlier.




MP3 Music Downloads

Preview songs, Download Free Music,Burn CDs at ITunes.com
iTunes_RGB_9mm

 


Google




InformationQuickFind.com - Find Information Fast

Links | Privacy Policy | News |