What question did this study set out to answer?

The study investigates the extension of D-types in lambda-homogeneous models through generic extension techniques.

June 17, 2026

Extending Types Preserving Diagrams

Puntos clave

The study investigates the extension of D-types in lambda-homogeneous models through generic extension techniques.
Consideration of D-type diagrams in lambda-homogeneous models.
Construction of a generic extension V from a model V0 of ZFC.
Analysis of conditions under which cardinals are preserved in the extension.
Each type in S can be extended to a D-type over B.
If a cardinal in V0 does not exceed lambda and lambda equals kappa plus, then it is preserved in V.
Conditions for the preservation of all cardinals of V0 in the extension V are established.

Resumen

We consider the question on diagram preserving extension of D -types. Let D denote the diagram of a -homogeneous model and let S be a set of D -types whose domains are subsets of cardinality less than of a suitable D -set B. We prove that a model V₀ of the set theory ZFC admits a generic extension V such that each type in S extends to a D -type over B ; moreover, if a cardinal of V₀ does not exceed and = ^+ then it is preserved in V. We also find conditions for preservation of all cardinals of V₀ in V.

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Cite This Study

K. Zh. Kudaĭbergenov (Sun,) studied this question.

synapsesocial.com/papers/6a323aead50b63ecad205b60 https://doi.org/https://doi.org/10.1134/s1055134426010050

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