An Introduction to Stability Theory
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.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
A C B A-automorphism algebraic assume atomic B D A big model Chapter cl(p cl(q classes clearly co-stable compactness consistent contradicts Corollary countable models defining schema Definition denote dim(p due to Shelah e-isolated e-prime e-saturated model elementary embedding elementary substructure elimination of quantifiers equivalence relation example Exercise fact finite subset forking extension forking symmetry formula G S(M G Sn heir of q implies independence property isolated isomorphism L-formula l-type L(A)-formula Lascar Lemma Let A C M Let p G S(A Let p(x Let q Let Tbe m-inconsistent Morley sequence mult(p n-tuples nonforking extension ofp Note notion parameters Poizat prime model Proposition 5.7 q G S(B rank realize q regular types RM(p satisfied stable theories stationary stp(b/A strongly minimal strongly regular superstable Suppose theorem Tis stable tp(b tp(b/M U tuple uncountable unique w-stable weakly orthogonal