{"product_id":"model-theory-and-near-rings-von-ahmed-yunis-abdelwanis","title":"Model Theory and Near Rings","description":"\u003cp\u003eWe recall some basic notions and facts from model theory. Let L be the fi?rst order language of near-rings. Two near-rings R and S are called elementarily equivalent if R and S satisfy the same fi?rst order sentences in L: A class C of near-rings is called elementarily closed if R is elementary equivalent to S; S belongs to C then R belongs to C. A class C of near-rings is called axiomatisable if C can be defi?end by a family of ?first order sentences in L. Also a class C is axiomatisable if C is elementarily closed and closed under the formation of ultra products. Further, a class C of near-rings is called fi?nitely axiomatisable if can be defi?end by a fi?rst order sentence in L. The fi?nitely axiomatisable classes can be characterized as follows : a class C of near-rings is fi?nitely axiomatisable if it is axiomatisable and the class of near-rings not in C is closed under formation of ultra products.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783659358203\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783659358203","offer_id":39448341413981,"sku":"9783659358203","price":39.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/44b8678a-be57-4492-8beb-00dffb29d7f3.jpg?v=1773468859","url":"https:\/\/shop.autorenwelt.de\/products\/model-theory-and-near-rings-von-ahmed-yunis-abdelwanis","provider":"Autorenwelt Shop","version":"1.0","type":"link"}