Related papers: Independence Results around Constructive ZF

This short note contains random thoughts about a factorization theorem for closure/interior operators on a powerset which is reminiscent to the notion of resolution for a monad/comonad. The question originated from formal topology but is…

In this paper we extend Fischler's quantitative generalization of Nesterenko's linear independence criterion, by weakening the hypotheses on the divisors of the coe cients of the linear forms and allowing (to some extent) the linear forms…

We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given property if and only if it has this property with respect to…

We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be.…

From N-tensor powers of the Toeplitz algebra, we construct a multipullback C*-algebra that is a noncommutative deformation of the complex projective space CP(N). Using Birkhoff's Representation Theorem, we prove that the lattice of kernels…

We show that in the theory ZF + DC + for every cardinal {\lambda}, the set of infinite subsets of {\lambda} is well-ordered (i.e., Shelah's AX4), the {\theta}-function measuring the surjective size of the powersets P({\kappa}) can take…

We follow up on Shi et al's (2020) and Cao's and my (2020) work on the local power of a new test for independence, Chatterjee (2019), and its relation to the local power properties of classical tests. We show quite generally that for…

In this paper we obtain a new class of transformation formulae (without an explicit presence of a derivative) for the integrals containing products of factors $|\zf|^2$ with respect to two components of a disconnected set on the critical…

We investigate large set axioms defined in terms of elementary embeddings over constructive set theories, focusing on $\mathsf{IKP}$ and $\mathsf{CZF}$. Most previously studied large set axioms, notably the constructive analogues of large…

In this paper we present a simpler proof of the fact that no inequality between $\mathrm{cof}(\mathcal{SN})$ and $\mathfrak{c}$ can be decided in ZFC by using well-known tecniques and results.

The aim of the paper is to first point out that the classical proof of the Freyd-Mitchell Embedding Theorem does not work in CZF; then, to propose an alternative embedding of a small abelian category into the category of sheaves of modules…

One of the motivations to state HRT conjecture on the linear independence of finite Gabor systems was the fact that there are linearly dependent Finite Wavelet Systems (FWS). Meanwhile, there are also many examples of linearly independent…

We show that there is an arithmetical formula F such that ZF proves that F is independent of PA and yet, unlike other arithmetical independent statements, the truth value of F cannot at present be established in ZF or in any other trusted…

We provide a differential-algebraic description of forking independence in the stable theory DCF$_{p,m}$ of differentially closed fields of characteristic $p>0$ with $m$-many commuting derivations. As a by-product of this description, we…

In this paper, we build Fidel-structures valued models following the methodology developed for Heyting-valued models; recall that Fidel structures are not algebras in the universal algebra sense. Taking models that verify Leibniz law, we…

We make use of a finite support product of the Jensen minimal forcing to define a model of set theory in which the separation theorem fails for projective classes $\mathbf\Sigma^1_n$ and $\mathbf\Pi^1_n$, for a given $n\ge3$.

The essentially non-free spectrum is the class of uncountable cardinals kappa in which there is an essentially non-free algebra of cardinality kappa which is almost free. In L, the essentially non-free spectrum of a variety is entirely…

Let G be a connected, reductive group over an algebraically closed field of good characteristic. For u in G unipotent, we describe the conjugacy classes in the component group A(u) of the centralizer of u. Our results extend work of the…

We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are $p$-divisible for infinitely many primes $p$, or…

Using elementary pcf, we show that there is no $j:V\to M,$ $M$ transitive, $j\lambda =\lambda >crit(j),$ $j^{\prime \prime}\lambda \in M.$