9 citations · 22 across the 12 of their papers we have counts for
13 papers
Non-absoluteness of Hjorth's Cardinal Characterization
Philipp Lücke, Ioannis Souldatos
In [5], Hjorth proved that for every countable ordinal , there exists a complete -sentence that has models of all cardinalities less than or equal to…
A Lower Bound for the Hanf Number for Joint Embedding
Will Boney, Ioannis Souldatos
In [13] the authors show that if is a strongly compact cardinal, is an Abstract Elementary Class (AEC) with , and satisfies joint embedding (amalgamation) cofi…
Non-Absoluteness of Model Existence at
David Milovich, Ioannis Souldatos
In [FHK13], the authors considered the question whether model-existence of -sentences is absolute for transitive models of ZFC, in the sense that if are…
Kurepa trees and spectra of -sentences
Dima Sinapova, Ioannis Souldatos
We use set-theoretic tools to make a model-theoretic contribution. In particular, we construct a \emph{single} -sentence that codes Kurepa trees to prove t…
Hanf Number for Scott Sentences of Computable Structures
Sergey Goncharov, Julia Knight, Ioannis Souldatos
The Hanf number for a set of sentences in (or some other logic) is the least infinite cardinal such that for all , if has models in all infinite car…
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…
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…
On automorphisms groups of structures of countable cofinality
Ioannis Souldatos
In [2] Su Gao proves that the following are equivalent for a countable (cf. theorem 1.2 too): (I)There is an uncountable model of the Scott sentence of . (II) There exists s…
Characterizing the powerset by a complete (Scott) sentence
Ioannis Souldatos
This paper is part II of a study on cardinals that are characterizable by a Scott sentence, continuing the work from http://arxiv.org/abs/1007.2426v1. A cardinal is characteriz…
Every set of first-order formulas is equivalent to an independent set
Ioannis Souldatos, I. Reznikoff
A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent set.
Independently Axiomatizable L_{omega_1,omega} Theories
Greg Hjorth, Ioannis Souldatos
In partial answer to a question posed by Arnie Miller (http://www.math.wisc.edu/~miller/res/problem.pdf) and X. Caicedo, we obtain sufficient conditions for an L_{omega_1,omega} th…
Linear Orderings and Powers of Characterizable Cardinal
Ioannis Souldatos
The current paper answers an open question of abs/1007.2426 We say that a countable model M characterizes an infinite cardinal kappa, if the Scott sentence of M has a model in card…
Notes on cardinals that are characterizable by a complete (Scott) sentence
Ioannis Souldatos
This is part I of a study on cardinals that are characterizable by Scott sentences. Building on [3], [6] and [1] we study which cardinals are characterizable by a Scott sentence $ϕ…