Related papers: The extender algebra and $\Sigma^2_1$-absoluteness
We show that for $\Pi_2$-properties of second or third order arithmetic as formalized in appropriate natural signatures the apparently weaker notion of forcibility overlaps with the standard notion of consistency (assuming large cardinal…
The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a…
We study the supersymmetric extension of the gauged $ O(3) $ sigma model in $ 2+1 $ dimensions and find the supersymmetry algebra. We also discuss soliton solutions in case the Maxwell term is replaced by the Born-Infeld term. We show that…
It is shown, from hypotheses in the region of $\omega^2$ Woodin cardinals, that there is a transitive model of KP + AD$_\mathbb{R}$ containing all reals.
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…
A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite dimensional Lie…
We extend to the context of algebraic groups a classic result on extensions of abstract groups relating the set of isomorphism classes of extensions of $G$ by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof should be…
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
In this work we construct a infinite dimensional $\ell$-super Galilean conformal algebra, which is a generalization of the $\ell=1$ algebra found in the literature. We give a classification of central extensions, the vector field…
It is proved that if $T$ is a $\Sigma_{n+1}$ Definable theory which is $\Sigma_n$-sound and extends $PA$, then $T$ can not prove the sentence $\Sigma_n-sound(T)$ that expresses the $\Sigma_n$-soundness of $T$. Optimality of this result is…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We prove that it is relatively consistent with the usual axioms of mathematics that all automorphisms of the Calkin algebra are inner. Together with a 2006 Phillips--Weaver construction of an outer automorphism using the Continuum…
It was recently shown that gl^(1|1) admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the…
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
In this paper we construct a graded universal enveloping algebra of a $G$-graded Lie algebra, where $G$ is not necessarily an abelian group. If the grading group is abelian, then it coincides with the classical construction. We prove the…
We introduce syzygies for derived categories and study their properties. Using these, we prove the derived invariance of the following classes of artin algebras: (1) syzygy-finite algebras, (2) Igusa-Todorov algebras, (3) AC algebras, (4)…
Foreman proved the Duality Theorem, which gives an algebraic characterization of certain ideal quotients in generic extensions. As an application he proved that generic supercompactness of $\omega_1$ is preserved by any proper forcing. We…
This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companionship. Specifically we develop here a general framework…
It is shown that the expansion methods developed in refs. arXiv:hep-th/0212347 and arXiv:hep-th/0401033v2 can be generalized so that they permit to study the expansion of algebras of loops, both when the compact finite-dimensional algebra…
Let $\Omega$ denote an algebra of sets and $\mu$ a $\sigma$-finite measure. We then prove that the completion of $\Omega$ under the pseudometric $d(A,B)$ = $\mu^{\ast}(A \triangle B)$ is $\sigma$-algebra isomorphic and isometric to the…