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Number of countable models

Journal of Symbolic Logic 43 (3):492-496 (1978)

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Types directed by constants.Predrag Tanović - 2010 - Annals of Pure and Applied Logic 161 (7):944-955.details Let T be a complete, countable, first-order theory having infinite models. We introduce types directed by constants, and prove that their presence in a model of T guaranties the maximal number of non-isomorphic countable models : I=2. Download Export citation Bookmark 3 citations
On constants and the strict order property.Predrag Tanović - 2006 - Archive for Mathematical Logic 45 (4):423-430.details Let T be a complete, countable, first-order theory with a finite number of countable models. Assuming that dcl(∅) is infinite we show that T has the strict order property. Download Export citation Bookmark 7 citations
Minimal first-order structures.Predrag Tanović - 2011 - Annals of Pure and Applied Logic 162 (11):948-957.details We prove a dichotomy theorem for minimal structures and use it to prove that the number of non-isomorphic countable elementary extensions of an arbitrary countable, infinite first-order structure is infinite. Download Export citation Bookmark 2 citations

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