逻辑

We introduce an operator on problems in Weihrauch complexity, which we call the inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a…

We consider the computational strength of Power-OTMs, i.e., ordinal Turing machines equipped with a power set operator, and study a notion of realizability based on these machines. When parameters are allowed, these machines are, modulo…

We investigate the ordinal invariants height, length, and width of well quasi orders (WQO), with particular emphasis on width, an invariant of interest for the larger class of orders with finite antichain condition (FAC). We show that the…

We study criteria for the existence of a dense or comeager conjugacy class in the automorphism group of a given measure on the Cantor space. We concentrate on good measures, defined by Akin [\emph{Trans.\ Amer.\ Math.\ Soc.} \textbf{357}…

In this paper, we introduce a concept of non-dependence of variables in formulas. A formula in first-order logic is non-dependent of a variable if the truth value of this formula does not depend on the value of that variable. This variable…

Dagger kernel categories, a powerful framework for studying quantum phenomena within category theory, provide a rich mathematical structure that naturally encodes key aspects of quantum logic. This paper focuses on the category SupOMLatLin…

Continuous functions on the unit interval are relatively tame from the logical and computational point of view. A similar behaviour is exhibited by continuous functions on compact metric spaces equipped with a countable dense subset. It is…

Club guessing principles were introduced by Shelah as a weakening of Jensen's diamond. Most spectacularly, they were used to prove Shelah's ZFC bound on the power of the first singular cardinal. These principles have found many other…

We follow the history and development of Brouwer's use of individual choice sequences up to the discovery of a method to apply them successfully in 1927. With the principles we derive from this first use we analyze in detail Brouwer's work…

In recent works by L. Drewnowski and I. Labuda and J. Mart\'inez et al., non-pathological analytic \( P \)-ideals and non-pathological \( F_\sigma \)-ideals have been characterized and studied in terms of their representations by a sequence…

We study maximal WAP and tame (in the sense of topological dynamics) quotients of $S_X(\mathfrak{C})$, where $\mathfrak{C}$ is a sufficiently saturated (called monster) model of a complete theory $T$, $X$ is a $\emptyset$-type-definable…

We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.

In the previously submitted version of this paper, available here for the record, we stated the following : "We give a self-contained proof of Isa Vialard's formula for $o(P\cdot Q)$ where $P$ and $Q$ are wpos. The proof introduces the…

How many odd numbers are there? How many even numbers? From Galileo to Cantor, the suggestion was that there are the same number of odd, even and natural numbers, because all three sets can be mapped in one-one fashion to each other. This…

This course introduces the fruitful links between model theory and a combinatoric of sets given by independence relations. An independence relation on a set is a ternary relation between subsets. Chapter 1 should be considered as an…

The following is a 2008 conjecture of Abraham, Bonnet and Kubi\'s: [ABK Conjecture] Every well quasi order (wqo) is a countable union of better quasi orders (bqo). We obtain a partial progress on the conjecture, by showing that the class of…

The common cause completeness (CCC) is a philosophical principle that asserts that if we consider two positively correlated events then it evokes a common cause. The principle is due to H. Reichenbach and has been largely studied in Boolean…

The Jensen-Steel core model is a canonical inner model which plays a fundamental role in the meta-mathematics of set theory. Its definition depends on exactly which hierarchy of fine-structural models of set theory, premice, one uses. Each…

I show that the strong negation is definable in 2Int, Wansing's bi-intuitionistic logic.

We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L\"uck's ultraproduct construction for team semantics and prove a suitable version of {\L}o\'s' Theorem.…