**Abstract:**

We modify the Einstein-Schrödinger theory to include a cosmological constant Λ_{z} which multiplies the symmetric metric. The cosmological constant Λ_{z} is assumed to be nearly cancelled by Schrödinger's cosmological constant Λ_{ b} which multiplies the nonsymmetric fundamental tensor, such that the total Λ = Λ_{z} + Λ_{ b} matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as |Λ_{z}| → ∞. For |Λ_{z}| ∼ 1/(Planck length)^{ 2} the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10^{-16} of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. An exact charged solution matches the Reissner-Nordström solution except for additional terms which are ∼ 10^{-66} of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory. Peri-center advance, deflection of light and time delay of light have a fractional difference of < 10^{-56} compared to Einstein-Maxwell theory for worst-case parameters. When a spin-1/2 field is included in the Lagrangian, the theory gives the ordinary Dirac equation, and the charged solution results in fractional shifts of < 10^{-50} in Hydrogen atom energy levels. Newman-Penrose methods are used to derive an exact solution of the connection equations, and to show that the charged solution is Petrov type-D like the Reissner-Nordström solution. The Newman-Penrose asymptotically flat [special characters omitted](1/*r*^{2}) expansion of the field equations is shown to match Einstein-Maxwell theory. Finally we generalize the theory to non-Abelian fields, and show that a special case of the resulting theory closely approximates Einstein-Weinberg-Salam theory.

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