Ultralogic Unification for Collections of Physical Theories

Let {S′Ni | i ∈ IN} represent a set of consequence operators defined on a language Λ, where each member of {S′Ni | i ∈ IN} corresponds to a science-community physical theory and each Ni is a S′Nj -system for each j ∈ IN. It is shown that there exists a hyperfinite ultralogic U ∈ ∗Cf defined on all internal subsets of Λ such that U 6 = U, and, for each i, j ∈ IN, S Ni ( ∗Nj) = U( ∗Nj). For each internal Y ⊂ Λ, ⋃ { S Ni (Y ) | i ∈ IN} ⊂ U(Y ) ⊂ Λ. Further, if finite X ⊂ Λ, then ⋃ { S Ni (X) | i ∈ IN} ⊂ U(X), and if each member of {S′Ni | i ∈ IN} is a practical consequence operator, then ⋃ {S Ni (X) | i ∈ IN} ⊂ U(X), and, for each i, j ∈ IN, S Ni (Nj) = U(Nj). Standard unifications for physical theories are also given.