One of the main goals in the study of the automorphism group Aut {Jt) of a countable, recursively saturated model Jt of Peano Arithmetic is to determine to what extent (the isomorphism type of) Jt is recoverable from (the isomorphism type of) Aut(^). A countable, recursively saturated model Jt of PA is characterized up to isomorphism by two invariants: its first-order theory Th(^ ) and its stan...

We describe a new general method for the computation of the group Aut(X) of self-homotopy equivalences of a space. It is based on the decomposition of Aut(X) induced by a factorization of X into a product of simpler spaces. Normally, such decompositions require assumptions (’induced equivalence property’, ’diagonalizability’), which are strongly restrictive and hard to check. In this paper we d...

We discuss some features of Einstein-Proca gravity in D = 3 and 4 spacetimes. Our study includes a discussion on the tree-level unitarity and on the issue of light deflection in 3D gravity in the presence of a mass term. 1 [email protected] 2 [email protected]

When is agreement possible? An important aspect of group decision-making is the question of how a group makes a choice when individual preferences may differ. Clearly, when making a single group choice, people cannot all have their “ideal” preferences, i.e, the options that they most desire, if those ideal preferences are different. However, for the sake of agreement, people may be willing to a...

We give an idea of the evolution of mathematical nonlinear geometric optics from its foundation by Lax in 1957, and present applications in various fields of mathematics and physics.

The paper is devoted to the study of topologies on the group Aut(X, B) of all Borel automorphisms of a standard Borel space (X, B). Several topologies are introduced and all possible relations between them are found. One of these topologies, τ , is a direct analogue of the uniform topology widely used in ergodic theory. We consider the most natural subsets of Aut(X, B) and find their closures. ...

We develop the method of iterated ultrapower representation to provide a unified and perspicuous approach for building automorphisms of countable recursively saturated models of Peano arithmetic PA. In particular, we use this method to prove Theorem A below, which confirms a long standing conjecture of James Schmerl. Theorem A. If M is a countable recursively saturated model of PA in which N is...

For a group G acting on set X, let $$\textrm{End}_G(X)$$ be the monoid of all G-equivariant transformations, or G-endomorphisms, and $$\textrm{Aut}_G(X)$$ its units. After discussing few basic results in general setting, we focus case when X are both finite order to determine smallest cardinality $$W \subseteq \textrm{End}_G(X)$$ such that \cup \textrm{Aut}_G(X)$$ generates ; this is known semi...

The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the direct sum of countably many copies of Z. In contrast, the group of automorphisms of a symbolic system of zero entropy seems to be highly constrained. Our mai...