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The goal is to prove that the axiom of choice is implied by the statement "for every infinite set : | | = | |".It is known that the well-ordering theorem is equivalent to the axiom of choice; thus it is enough to show that the statement implies that for every set there exists a well-order.
The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem; see the section "Weaker forms" below. Lowenheim-Skolem theorem : If first-order theory has infinite model, then it has infinite model of every possible cardinality greater than cardinality of language ...
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This is a list of terrestrial ecoregions as compiled by the World Wildlife Fund (WWF). The WWF identifies terrestrial, freshwater, and marine ecoregions. The terrestrial scheme divides the Earth's land surface into 8 biogeographic realms, containing 867 smaller ecoregions. Each ecoregion is classified into one of 14 major habitat types, or biomes.
The village categories for some countries are combined with categories for other types of settlements because no official distinction is made locally. See also: Category:Populated places by country Subcategories
Village or Tribe – a village is a human settlement or community that is larger than a hamlet but smaller than a town. The population of a village varies; the average population can range in the hundreds. Anthropologists regard the number of about 150 members for tribes as the maximum for a functioning human group.
This page contains a list of model villages in the UK and Ireland. You might also want to look at Company town. This category is for full size villages, typically built for factory workers. For miniature villages, use Category:Miniature parks.
Anthropogenic biomes, also known as anthromes, human biomes or intensive land-use biome, describe the terrestrial biosphere in its contemporary, human-altered form using global ecosystem units defined by global patterns of sustained direct human interaction with ecosystems. Anthromes are generally composed of heterogeneous mosaics of different ...