We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality r...

We investigate the field theory of strings having as a target space an arbitrary discrete onedimensional manifold. The existence of the continuum limit is guaranteed if the target space is a Dynkin diagram of a simply laced Lie algebra or its affine extension. In this case the theory can be mapped onto the theory of strings embedded in the infinite discrete line ZZ which is the target space of ...

The non-Abelian analog of the classical Coulomb gas is discussed. The statistical mechanics of arrays of classical particles which transform under various representations of a non-Abelian gauge group and which interact through non-Abelian electric fields are considered. The problem is formulated on the lattice and, for the case of adjoint charges, it is solved in the large N limit. The explicit...

ground state geometries have been computed using density functional theory (dft) at b3lyp/6-31g(d,p) level of theory. the excitation energies and spectroscopic parameters have been computed using long range corrected (lc) hybrid functional by time dependent density functional theory (tddft) with lc-blyp level of theory. the polarizable continuum model (pcm) has been used for evaluating bulk sol...

In a paper of 1929, Banach and Kuratowski proved—assuming the continuum hypothesis—a combinatorial theorem which implies that there is no nonvanishing σ-additive finite measure μ on R which is defined for every set of reals. It will be shown that the combinatorial theorem is equivalent to the existence of a K-Lusin set of size 20 and that the existence of such sets is independent of ZFC + ¬CH.