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Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.10 Stable Sorting

6.10 Stable Sorting A sorting algorithm is stable when equal keys keep their original relative order. Stability is not part of the basic sorting contract, because an unstable output may still be ordered and may still be a permutation of the input. Stability is an additional semantic guarantee about records, identities, and secondary fields. Problem You have records with keys, and two records may have equal keys but different attached...
algorithms sorting stability May 4, 2026
Maths › 03. Logic and Foundations ›

6.4 Stability

Stability theory studies the complexity of first order theories by analyzing how types behave over parameter sets, and in particular by measuring how many distinct types exist and how these types interact with definable sets. The guiding idea is that a theory should be considered tame if the space of types is controlled, and wild if the space of types grows too quickly or exhibits arbitrary combinatorial patterns. Throughout this...
logic model theory stability types May 2, 2026
Maths › 03. Logic and Foundations ›

6.5 Classification

Classification theory studies first order theories by organizing them according to the complexity of their definable sets and types, with the goal of distinguishing theories that admit a systematic structural description from those whose models exhibit uncontrolled combinatorial behavior. The central principle is that the behavior of formulas, when evaluated across different parameter configurations, determines the global structure of models, and therefore one can classify theories by analyzing the combinatorial...
logic model theory classification theory stability May 2, 2026