An Introduction to Stability TheoryCourier Corporation, 17.05.2013 - 160 Seiten This introductory treatment covers the basic concepts and machinery of stability theory. Lemmas, corollaries, proofs, and notes assist readers in working through and understanding the material and applications. Full of examples, theorems, propositions, and problems, it is suitable for graduate students in logic and mathematics, professional mathematicians, and computer scientists. Chapter 1 introduces the notions of definable type, heir, and coheir. A discussion of stability and order follows, along with definitions of forking that follow the approach of Lascar and Poizat, plus a consideration of forking and the definability of types. Subsequent chapters examine superstability, dividing and ranks, the relation between types and sets of indiscernibles, and further properties of stable theories. The text concludes with proofs of the theorems of Morley and Baldwin-Lachlan and an extension of dimension theory that incorporates orthogonality of types in addition to regular types. |
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algebraic assume b₁ b₂ big model cardinality Chapter cl(p cl(q clearly coheir compactness consistent contradicts Corollary countable models d₁ defining schema Definition denote dim(p due to Shelah E S(B E S(M e-isolated e-prime e-saturated model elementary embedding elementary substructure elimination of quantifiers equivalence relation ES(A ES(M example Exercise extension of q follows forking extension forking symmetry heir of q implies independence property induction isolated L-formula L(A)-formula Lascar Lemma Let ā Let p E S(A Let p(x Let q m-inconsistent M₁ Morley sequence mult(p n-tuples nonforking extension Note notion p₁ and p2 p₂ parameters Poizat prime model Proof Proposition 5.7 proved q ES(B rank realize q RM(p Rº(p S₁(M satisfied stable theories stationary stp(ā/A stp(b/B strongly minimal strongly regular superstable Suppose theorem tp(ā tp(b tuple w-stable weakly orthogonal