Related papers: On NSOP$_2$ Theories
We recall the importance of recognizing the different mathematical nature of various concepts relating to PT-symmetric quantum theories. After clarifying the relation between supersymmetry and pseudo-supersymmetry, we prove generically that…
The conditions for fully supersymmetric backgrounds of general N=2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a…
We provide a model-theoretic classification of the countable homogeneous $\mathbf{H}_4$-free 3-hypertournament studied by Cherlin, Hubi\v{c}ka, Kone\v{c}n\'y, and Ne\v{s}et\v{r}il. Our main result is that the theory of this structure is…
We put into a general setting a technique of Rene' David (see "A Very Absolute Pi^1_2 Singleton, Annals of Pure and Applied Logic, 1982) to show that for S a Sigma^1_1 statement quantifying over subclasses of V of a special form, there is a…
We construct the $N=2$ super $W_4$ algebra as a certain reduction of the second Gel'fand-Dikii bracket on the dual of the Lie superalgebra of $N=1$ super pseudo-differential operators. The algebra is put in manifestly $N=2$ supersymmetric…
We prove Los conjecture = Morley theorem in ZF, with the same characterization (of first order countable theories categorical in aleph_alpha for some (equivalently for every) ordinal alpha>0. Another central result here is, in this context:…
A new case of Shelah's eventual categoricity conjecture is established: $\mathbf{Theorem}$ Let $K$ be an AEC with amalgamation. Write $H_2 := \beth_{\left(2^{\beth_{\left(2^{\text{LS} (K)}\right)^+}}\right)^+}$. Assume that $K$ is…
After certain subsets of Natural numbers called Range and Row are defined, we assume (1) there is a function that can produce prime numbers and (2) each even number greater than 2, like A, can be represented as the sum of n prime numbers.…
The Ramanujan $_1\psi_1$ summation theorem in studied from the perspective of $q$-Jackson integrals, $q$-difference equations and connection formulas. This is an approach which has previously been shown to yield Bailey's very-well-poised…
This is an expository work presenting in detail the proof of the structure theorem for divisible abelian groups. A divisible abelian group is an abelian group that satisfies nD=D for all natural n. The theorem states that any divisible…
We construct a superpotential for the general N=1/2 supersymmetric gauge theory coupled to chiral matter in the fundamental and adjoint representations, and investigate the one-loop renormalisability of the theories.
A theory T is tight if different deductively closed extensions of T (in the same language) cannot be bi-interpretable. Many well-studied foundational theories are tight, including PA [Visser2006], ZF, Z2, and KM [enayat2017]. In this…
We prove that N=2 theories that arise by taking n free hypermultiplets and gauging a subgroup of Sp(n), the non-R global symmetry of the free theory, have a remaining global symmetry which is a direct sum of unitary, symplectic, and special…
The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories…
A Ramsey-like theorem is a statement of the form ``For every 2-coloring of $[\mathbb{N}]^2$, there exists an infinite set~$H \subseteq \mathbb{N}$ such that $[H]^2$ avoids some pattern''. We prove that none of these statements are…
We study several different $Z_2$ topological ordered states in frustrated spin systems. The effective theories for those different Z_2 topological orders all have the same form -- a Z_2 gauge theory which can also be written as a mutual…
We suggest a method of bosonizing any D=2 theory. We demonstrate how it works with the examples of the Thirring and the Schwinger models, known results are reproduced. This method, being applied to the Gross-Neveu model, yields nonlinear…
We show that every unstable NIP theory admits a V-definable linear quasi-order, over a finite set of parameters. In particular, if the theory is omega-categorical, then it interprets an infinite linear order. This partially answers a…
We provide an essentially complete dictionary of all implications among the basic and fundamental conditions in weighted theory such as the doubling, one weight A_p(w), A_\infty and C_p conditions as well as the two weight A_p and the…
Motivated by the theory of proof complexity generators we consider the following $\Sigma^p_2$ search problem $\mbox{DD}_P$ determined by a propositional proof system $P$: given a $P$-proof $\pi$ of a disjunction $\bigvee_i {\alpha}_i$, no…