{"product_id":"9780792343660","title":"Mathematics and Its Applications","description":"\u003ch1\u003eMathematics and Its Applications\u003c\/h1\u003e \u003ch2\u003eWeaver, George\u003c\/h2\u003e \u003cp\u003eHenkin-Keisler models emanate from a modification of the  Henkin construction introduced by Keisler to motivate the definition  of ultraproducts. Keisler modified the Henkin construction at that  point at which `new' individual constants are introduced and did so in  a way that illuminates a connection between Henkin-Keisler  models and ultraproducts. The resulting construction can be viewed  both as a specialization of the Henkin construction and as an  alternative to the ultraproduct construction. These aspects of the  Henkin-Keisler construction are utilized here to present a  perspective on ultraproducts and their applications accessible to the  reader familiar with Henkin's proof of the completeness of first order  logic and naive set theory. This approach culminates in proofs of  various forms of the Keisler-Shelah characterizations of  elementary equivalence and elementary classes via  Henkin-Keisler models. The presentation is self-contained and  proofs of more advanced results from set theory are introduced as  needed. \u003cbr\u003e  \u003cem\u003eAudience:\u003c\/em\u003e Logicians in philosophy, computer science, linguistics  and mathematics.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1997-01-31\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780792343660\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/b102616\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 258\u003c\/p\u003e ","brand":"Springer US","offers":[{"title":"Default Title","offer_id":46539710333068,"sku":"9780792343660","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780792343660.jpg?v=1775679564","url":"https:\/\/lateknightbooks.com\/products\/9780792343660","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}