Related papers: Mahlo classes for first-order reflections

We construct $P(phi)_1$-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ…

In this paper, we prove the multiplicativity of the K\"unneth spectral sequence. This is established by an analogue of the Comparison Theorem from homological algebra, which we suspect may be useful for other spectral sequences. This…

We study various universal-existential fragments of first-order theories of fields, in particular of function fields and of equicharacteristic henselian valued fields. For example we discuss to what extent the theory of a field k determines…

We investigate the descriptive complexity of the set of models of first-order theories. Using classical results of Knight and Solovay, we give a sharp condition for complete theories to have a $\pmb\Pi_\omega^0$-complete set of models. In…

For a Latt\`es map $\phi:\mathbb P^1 \to \mathbb P^1$ defined over a number field $K$, we prove a conjecture on the integrality of points in the backward orbit of $P\in \mathbb P^1(\overline K)$ under $\phi$.

We investigate the set of Pi-1-2 sentences which are Pi-1-1 conservative over the theories of reverse mathematics RCA0+ISigma_n and ACA0. We exhibit new elements of these sets and conclude that the sets are Pi_2 complete. Along the way, we…

This paper aims to systematically study mystic reflection groups that emerged independently in the paper [Selecta Math. (N.S.) 14 (2009), 325-372, arXiv:0806.0867] by the authors and in the paper [Algebr. Represent. Theory 13 (2010),…

We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\big |…

We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…

The kinetic field theory is developed without assumptions of statistical homogeneity and isotropy. In a solvable toy model with short-ranged interactions, we compare first-order perturbation theory to an iterated mean-field approximation…

The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping…

We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.

Modulo the existence of large cardinals, there is a model of set theory in which for some set $B$ of regular cardinals, the sequence $\langle \text{pcf}^\alpha(B): \alpha \in \text{Ord} \rangle$ is strictly increasing. The result answers a…

Progression, the task of updating a knowledge base to reflect action effects, generally requires second-order logic. Identifying first-order special cases, by restricting either the knowledge base or action effects, has long been a central…

A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…

We obtain order estimates for the best uniform orthogonal trigonometric approximations of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}, \ 1\leq p<\infty$, in case at consequences…

We classify the computability-theoretic complexity of two index sets of classes of first-order theories: We show that the property of being an $\aleph_0$-categorical theory is $\Pi^0_3$-complete; and the property of being an Ehrenfeucht…

Let O_K be the ring of integers of a finite extension K of Q_p. Given two reflexive F-gauges on O_K, we show that for large enough n, the mod p^n-reductions of their first syntomic cohomology groups, which might be regarded as a refinement…

Let A be an arbitrary ring. We introduce a Dennis trace map mod n, from K_1(A;Z/n) to the Hochschild homology group with coefficients HH_1(A;Z/n). If A is the ring of integers in a number field, explicit elements of K_1(A,Z/n) are…

We investigate the reflection theory of Nichols algebras over arbitrary coquasi-Hopf algebras with bijective antipode, generalizing previous results restricted to the pointed cosemisimple setting [47]. By establishing a braided monoidal…