Related papers: $\Sigma^1_3$ sets in the Sacks model

Let $\mathcal R$ be a $\Sigma^1_1$ binary relation, and recall that a set $A$ is $\mathcal R$-discrete if no two elements of $A$ are related by $\mathcal R$. We show that in the Sacks and Miller forcing extensions of $L$ there is a…

In this paper we study M-theory compactifications on seven-dimensional manifolds with SU(3) structure. As such manifolds naturally pick out a specific direction, the resulting effective theory can be cast into a form which is similar to…

Kontsevich conjectured that $\text{BDiff}(M, \text{rel }\partial)$ has the homotopy type of a finite CW complex for all compact $3$-manifolds with non-empty boundary. Hatcher-McCullough proved this conjecture when $M$ is irreducible. We…

In this note, we show that, under a certain condition, solvable extensions of number fields ramifed at only one prime are Ostrowski. As a corollary, we deduce a generalization of Hilbert Theorem 94 to cyclic extensions ramifed at one prime.

The classical Theorem of Mumford states that a topologically regular complex algebraic surface in $\mathbb{C}^3$ with an isolated singular point is smooth. We proof that any Lipschitz regular complex algebraic set is smooth. No restriction…

It was recently demonstrated that the N=0,1,2,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realizations to the finite-dimensional (super)conformal groups SL(2,R), OSp(1|2), SU(1,1|1), and SU(1,1|2),…

We introduce a set of consistency conditions on the S-matrix of theories of massless particles of arbitrary spin in four-dimensional Minkowski space-time. We find that in most cases the constraints, derived from the conditions, can only be…

We derive a family of correctness conditions for complex Langevin simulations. In particular, we show that if in a given theory the expectation values of all observables within a particular space satisfy the theory's Schwinger-Dyson…

Let $K$ be a number field, let $S$ be the set of all normalized, non-conjugate Archimedean valuations of $K$, and let $K_{S} = \prod_{v \in S} K_v$ be the Minkowski space associated with $K$. We strengthen recent results of…

In this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish that the sets of solvable groups,…

Based on results obtained in a companion paper [MSRI preprint 1997-002], we construct groups of special $S$--units for function fields of characteristic $p>0$, and show that they satisfy Gras--type Conjectures. We use these results in order…

For a smooth $k$-dimensional submanifold $\Sigma$ of a $d$-dimensional compact Riemannian manifold $M$, we extend the $L^p(\Sigma)$ restriction bounds of Burq-G\'erard-Tzvetkov -- originally proved for individual Laplace--Beltrami…

We introduce a new topological generalization of the $\sigma$-projective hierarchy, not limited to Polish spaces. Earlier attempts have replaced $^{\omega}\omega$ by $^{\kappa}\kappa$, for $\kappa$ regular uncountable, or replaced countable…

It is argued that a phenomenologically viable grand unification model from superstring is $SU(3)^3$, the simplest gauge group among the grand unifications of the electroweak hypercharge embedded in semi-simple groups. We construct a…

We construct globally-defined $SU(3)$ structures on smooth compact toric varieties (SCTV) in the class of $\mathbb{CP}^1$ bundles over $M$, where $M$ is an arbitrary SCTV of complex dimension two. The construction can be extended to the…

We prove that the ideal in complex cobordism ring $\MU^*$ generated by the polynomial generators $S=(x_1, x_k, k\geq 3)$ of $c_1$-spherical cobordism ring $W^*$, viewed as elements in $\MU^*$ by forgetful map is prime. Using the…

In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…

This paper is devoted to various applications of Hardy-Sobolev type inequalities. We derive a new $L^2$ estimate for the $\bar{\partial}-$equation on ${\mathbb C}^n$ which yields a quantitative generalization of the Hartogs extension…

In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3--manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we obtain the first…

In this article we will investigate nonmeasurability with respect to some $\sigma$-ideals in Polish space $X,$ of images of subsets of $X$ by selected mappings defined on the space $X$. Among of them we answer the following question: "It is…