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 (...) also prove that if $\aleph_{\alpha}$ is characterized by a Scott sentence, at least one of $\aleph_{\alpha}$, $\aleph_{\alpha+1}$, or $$ is homogeneously characterizable. Based on an argument of Shelah, we give counterexamples that characterizable cardinals are not closed under predecessors or cofinalities. (shrink)

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.

We use set-theoretic tools to make a model-theoretic contribution. In particular, we construct a single \-sentence \ that codes Kurepa trees to prove the following statements: The spectrum of \ is consistently equal to \ and also consistently equal to \\), where \ is weakly inaccessible.The amalgamation spectrum of \ is consistently equal to \ and \\), where again \ is weakly inaccessible. This is the first example of an \-sentence whose spectrum and amalgamation spectrum are consistently both right-open and (...) right-closed. It also provides a positive answer to a question in Souldatos :533–551, 2014).Consistently, \ has maximal models in finite, countable, and uncountable many cardinalities. This complements the examples given in Baldwin et al. :545–565, 2016) and Baldwin and Souldatos :444–452, 2019) of sentences with maximal models in countably many cardinalities.Consistently, \ and there exists an \-sentence with models in \, but no models in \. This relates to a conjecture by Shelah that if \, then any \-sentence with a model of size \ also has a model of size \. Our result proves that \ can not be replaced by \, even if \. (shrink)

In partial answer to a question posed by Arnie Miller [4] and X. Caicedo [2] we obtain sufficient conditions for an ℒω1,ω theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every ℒω1,ω theory in a countable language has an independent axiomatization. The second, this time outright in ZFC, every intersection of a family of Borel sets can be formed as the intersection of a family of independent Borel sets.

In this article we consider certain elements of the normative theory of Jürgen Habermas in the light of the proposals of Bruce Ackerman, with a view to strengthening a concept of deliberative democracy applied to the legitimation of juridical rules. We do not construct a hierarchy of the two positions, but seek to bring together certain elements to achieve a common project. As the starting point for examining the work of the two authors, we take the scheme proposed by Habermas (...) in Faktizität und Geltung. In this connection, through the work of Ackerman, we intend to fill in some of the gaps that Habermas appears to have left in the theory of radical democracy applied to the law. The work of Ackerman can make a significant contribution to deliberative democracy, to the discourse principle that Habermas defines, and to the contractualist theories from a liberal perspective. The study of these contributions makes possible a critical judgment that enables the legitimation of juridical rules carried out by Habermas to acquire greater practicity. In examining the epistemological status of juridical science and law, we attempt to determine the weight and the performance of normative democracy. In Tarr's view, it is a matter for philosophers to examine direct democracy and its desirability. (shrink)

James I. The Political Works of James I. Reprinted from the Edition of 1616. With an Introduction by Charles Howard McIlwain. Cambridge: Harvard University Press, 1918. cxi, 354 pp. Reprinted 2002 by The Lawbook Exchange, Ltd.

t. 1. Rasshiri︠a︡i︠u︡shchai︠a︡si︠a︡ vselennai︠a︡ absoli︠u︡ta -- t. 2. Kosmo-antropo-sot︠s︡io-prirodogenez cheloveka -- t. 3. Antropologicheskai︠a︡ istoriosofii︠a︡.