1 - 10 of 12 articles
We prove that Basic Arithmetic, BA, has the de Jongh property, i.e., for any propositional formula A(p
) built up of atoms p
) if and only if for all arithmetical sentences B
We present a model where ω
1 is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more recently continued by Schrittesser and Friedman (see ),...
We establish that, in ZF (i.e., Zermelo–Fraenkel set theory minus the Axiom of Choice AC), the statement
RLT: Given a set
and a non-empty set
of non-empty elementary closed subsets of 2
satisfying the fip, if
has a choice function, then...
We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies (of various complexity) have been extensively studied, we point out that (if...
Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct...
We obtain an improvement of some coloring theorems from Eisworth (Fund Math 202:97–123, 2009; Ann Pure Appl Logic 161(10):1216–1243, 2010), Eisworth and Shelah (J Symb Logic 74(4):1287–1309, 2009) for the case where the singular cardinal in question has countable cofinality. As a corollary, we...
Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC). However, her factor is unnatural in the sense that it is constructed in an ad hoc manner. We present a more natural example of such a factor. We also show that the theory of...
I study definability and types in the linear fragment of continuous logic. Linear variants of several definability theorems such as Beth, Svenonus and Herbrand are proved. At the end, a partial study of the theories of probability algebras, probability algebras with an aperiodic automorphism and...
We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation
, which is a weak subtheory of Grzegorczyk’s theory
, is a minimal...
We address three questions raised by Cummings and Foreman regarding a model of Gitik and Sharon. We first analyze the PCF-theoretic structure of the Gitik–Sharon model, determining the extent of good and bad scales. We then classify the bad points of the bad scales existing in both the...
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