Strongly dependent theories
Saharon Shelah
TL;DR
This paper explores properties of strongly dependent theories in model theory, demonstrating that large indiscernible sequences exist under certain cardinality conditions, extending previous results in the field.
Contribution
It advances understanding of indiscernible sequences in strongly dependent theories, building on prior work to establish new cardinality bounds.
Findings
Existence of large indiscernible sequences in models of strongly dependent theories.
Extension of previous results in model theory regarding indiscernibility.
Cardinality bounds for indiscernible sequences in models of such theories.
Abstract
We further investigate the class of models of a strongly dependent (first order complete) theory T, continuing math.LO/0406440. If |A|+|T|<= mu, I subseteq C, |I| >=beth_{|T|^+}(mu) then some J subseteq I of cardinality mu^+ is an indiscernible sequence over A .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory