Switch to: References

Citations of:

Linear orderings and powers of characterizable cardinals

Ioannis Souldatos

Annals of Pure and Applied Logic 163 (3):225-237 (2012)

Add citations

You must login to add citations.

Notes on Cardinals That Are Characterizable by a Complete (Scott) Sentence.Ioannis Souldatos - 2014 - Notre Dame Journal of Formal Logic 55 (4):533-551.details This is the first part of a study on cardinals that are characterizable by Scott sentences. Building on previous work of Hjorth, Malitz, and Baumgartner, we study which cardinals are characterizable by a Scott sentence $\phi$, in the sense that $\phi$ characterizes $\kappa$, if $\phi$ has a model of size $\kappa$ but no models of size $\kappa^{+}$. We show that the set of cardinals that are characterized by a Scott sentence is closed under successors, countable unions, and countable products. We (...) Download Export citation Bookmark 3 citations
Complete Lω1,ω‐sentences with maximal models in multiple cardinalities.John Baldwin & Ioannis Souldatos - 2019 - Mathematical Logic Quarterly 65 (4):444-452.details In [5], 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 sentences. In this paper, we give examples of complete ‐sentences with maximal models in more than one cardinality. From (homogeneous) characterizability of κ we construct sentences with maximal models in κ and in one of and more. Indeed, consistently we find sentences with maximal models in uncountably many distinct cardinalities. Download Export citation Bookmark 3 citations

1