Partitioning subsets of stable models
Copyright policy )Partitioning subsets of stable models
Abstract.This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into ∣B∣<κ(T) pieces. 〈Ai ∣ i < ∣B∣<κ(T)〉. such that for each Ai there is a Bi ⊆ B where ∣Bi∣ < κ(T) and , Second, if A and B are as above and ∣A∣ > ∣B∣, then we try to find A′ ⊂ A and B′ ⊂ B such that ∣A′∣ is as large as possible. ∣B′∣ is as small as possible, and . We prove some positive results in this direction, and we discuss the optimality of these results under ZFC + GCH.
- University of California, Los Angeles United States
- University of Notre Dame United States
partition result for subsets of stable models, stable theories, Classification theory, stability, and related concepts in model theory, stability, two cardinal problems
partition result for subsets of stable models, stable theories, Classification theory, stability, and related concepts in model theory, stability, two cardinal problems
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