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An analogue of U-rank for atomic classes by Baldwin, John T.; Laskowski, Michael C.; Shelah, Saharon is a scholarly article available to read on EtoBox.

What is An analogue of U-rank for atomic classes about?

For a countable, complete, first-order theory $T$, we study $At$, the class of atomic models of $T$. We develop an analogue of $U$-rank and prove two results. On one hand, if some tp(d/a) is not ranked, then there are $2^{\aleph_1}$ non-isomorphic models in $At$ of size $\aleph_1$. On the other hand, if all types have finite rank, then the rank is fully additive and every finite tuple is dominated by an independent set of realizations of pseudo-minimal types.

Author

Baldwin, John T.; Laskowski, Michael C.; Shelah, Saharon

Published

2025

Language

EN