逻辑

We make use of generalized iterations of Jensen forcing to define a cardinal-preserving generic model of ZF for any $n\ge 1$ and each of the following four Choice hypotheses: (1)…

We introduce simulations for modal logics with subclassical negations and restoration modalities, establish an adequacy theorem, and prove intrinsic (Hennessy-Milner-type) and relative (Van Benthem-type) characterization results. These…

We work in the realm of sets of reals. We prove that in the Miller model and in a model constructed by Goldstern-Judah-Shelah all universally meager sets have size at most $\omega_1$. Some relations between combinatorial covering properties…

We study valued fields equipped with an automorphism. We prove that all of them have an extension admitting an equivariant cross-section of the valuation. In residual characteristic zero, and in the presence of such a cross-section, we show…

We propose a multi-agent epistemic logic capturing reasoning with degrees of plausibility that agents can assign to a given statement, with $1$ interpreted as "entirely plausible for the agent" and $0$ as "completely implausible" (i.e., the…

In a classical paper by Ben-David and Magidor, a model of set theory was exhibited in which $\aleph_{\omega+1}$ carries a uniform ultrafilter that is $\theta$-indecomposable for every uncountable cardinal $\theta<\aleph_\omega$. In this…

It is shown that the isomorphism relation between continuous t-norms is Borel bireducible with the relation of order isomorphism between linear orders on the set of natural numbers, and therefore, it is a Borel complete equivalence…

Hrushovski proved the Lie model theorem in full generality with model theoretic methods. The theorem states that for every approximate group there exists a generalized definable locally compact model, which, simplifying, is a…

We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…

Komjath studied the list chromatic number of infinite graphs and introduced the notion of restricted list chromatic number. For a graph $X=(V_X,E_X)$ and a cardinal $\kappa$, we say that $X$ is restricted list colorable for $\kappa$ if for…

This article is concerned with finite rank stability theory, and more precisely two classical ways to decompose a type using minimal types. The first is its domination equivalence to a Morley power of minimal types, and the second its…

Kinna--Wagner Principles state that every set can be mapped into some fixed iterated power set of an ordinal, and we write $\mathsf{KWP}$ to denote that there is some $\alpha$ for which this holds. The Kinna--Wagner Conjecture, formulated…

Non-compact proofs are a class of reasoning that is used in mathematics but overlooked in the analysis of (un)provability of consistency. We focus on proofs of arithmetical statements (*) "for any natural number n, F(n)." A proof of (*) is…

In his study of the Ultrapower Axiom (UA), Goldberg revealed a connection between UA and the determinacy of certain games that witness Lipschitz reducibility between ultrafilters. In particular, he analyzed the relationship between the…

Let $\Aut(G)$ denote the group of (bi-)continuous automorphisms %and $\Out(G)$ the outer automorphism group of a non-Archimedean Polish group~$G$. We show that for any such $G$ with an invariant countable basis of open subgroups, the group…

We identify a strong structural obstruction to Uniform Separation in constructive arithmetic. The mechanism is independent of semantic content; it emerges whenever two distinct evaluator predicates are sustained in parallel and inference…

We continue our work on the model theory of free lattices, solving two of the main open problems from our first paper on the subject. Our main result is that the universal (existential) theory of infinite free lattices is decidable. Our…

We present a new proof of descent for stably dominated types in any theory, dropping the hypothesis of the existence of global invariant extensions. Additionally, we give a much simpler proof of descent for stably dominated types in…

A normal modal logic is pretransitive, if the modality corresponding to the transitive closure of an accessibility relation is expressible in it. In the present work we establish the finite model property for pretransitive generalizations…

One of the better-known independence results in general mathematics is Shelah's solution to Whitehead's problem of whether $\mathrm{Ext}^1(A,\mathbb{Z})=0$ implies that an abelian group $A$ is free. The point of departure for the present…