2 citations · 7 across the 20 of their papers we have counts for
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Hanf Numbers and Presentation Theorems in AECs
Will Boney, John Baldwin
We prove that a strongly compact cardinal is an upper bound for a Hanf number for amalgamation, etc. in AECs using both semantic and syntactic methods. To syntactically prove non-d…
Complete -Sentences with Maximal Models in Multiple Cardinalities
John Baldwin, Ioannis Souldatos
In [BKS15] examples of incomplete sentences are given with maximal models in more than one cardinality. The question was raised whether one can find similar examples of complete se…
Constructing many atomic models in
John T. Baldwin, Michael C. Laskowski, Saharon Shelah
We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of . Theorem: Let be any co…
The Joint Embedding Property and Maximal Models
John T. Baldwin, Martin Koerwien, Ioannis Souldatos
We introduce the notion of a `pure` Abstract Elementary Class to block trivial counterexamples. We study classes of models of bipartite graphs and show: Main Theorem (cf. Theorem 3…