Related papers: Von Neumann coordinatization is not first-order
For every partially ordered sets I, having a finite cofinal subset, and every field K we build a unital, locally matricial and hence unit-regular K-algebra B(I) such that the lattice of all its ideals is order isomorphic to the lattice of…
Generalizing von Neumann's result on type II$_1$ von Neumann algebras, we characterize lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally…
We characterize the order of principal congruences of a bounded lattice as a bounded ordered set. We also state a number of open problems in this new field.
We consider various sufficiently nonlinear sigma models for nematic liquid crystal ordering of RP^{N-1} type and of lattice gauge type with continous symmetries. We rigorously show that they exhibit a first-order transition in the…
This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a…
We investigate the lattice L(V) of subspaces of an m-dimensional vector space V over a finite field GF(q) with q being the n-th power of a prime p. It is well-known that this lattice is modular and that orthogonality is an antitone…
The Cauchy problem for first order system $L(t, x, \D_t, \D_x)$ is known to be well posed in $L^2$ when a it admits a microlocal symmetrizer $S(t,x, \xi)$ which is smooth in $\xi$ and Lipschitz continuous in $(t, x)$. This paper contains…
We reprove and generalize in a combinatorial way the result of A. Bj\"orner [J.\ Comb.\ Th.\ A {\bf 30}, 1981, pp.~90--100, Theorem 3.3], that order complexes of noncomplemented lattices are contractible, namely by showing that these…
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting…
This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…
We characterize vector lattices in which unbounded order convergence is eventually order bounded. Among other things, the characterization provides a solution to \cite[Probl.23]{Az}.
We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number of open problems in this new field.
We consider the ring $\mathbb Z_n$ (integers modulo $n$) with the partial order `$\leq$' given by `$a \leq b$ if either $a=b$ or $a\equiv ab~(mod~n)$'. In this paper, we obtain necessary and sufficient conditions for the poset ($\mathbb…
We present a unification problem based on first-order syntactic unification which ask whether every problem in a schematically-defined sequence of unification problems is unifiable, so called loop unification. Alternatively, our problem may…
In [6] we proved that the universal theory of infinite free lattices is (algorithmically) decidable, leaving open the problem of decidability of the full theory of an (infinite) free lattice. We solve this problem by proving that, for every…
We introduce the notion of first order amenability, as a property of a first order theory $T$: every complete type over $\emptyset$, in possibly infinitely many variables, extends to an automorphism-invariant global Keisler measure in the…
Let (L_i : i\in I) be a family of lattices in a nontrivial lattice variety V, and let \phi_i: L_i --> M, for i\in I, be isotone maps (not assumed to be lattice homomorphisms) to a common lattice M (not assumed to lie in V). We show that the…
The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (e.g., $\{0\})$ that are closed under the natural metric, but has no prime ideals closed under that metric; hence closed…
Using Popa's deformation/rigidity theory, we investigate prime decompositions of von Neumann algebras of the form $L(\mathcal{R})$ for countable probability measure preserving equivalence relations $\mathcal{R}$. We show that…